Tootfinder

@… Hope the eye is feeling a bit better today. Here is a joke that is right up your alley 😄
https://infosec.exchange/@nuthatch/112028698666082…

This https://arxiv.org/abs/2305.13148 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A characterization of horizontally totally geodesic hypersurfaces in Heisenberg groups
In this paper we achieve a first concrete step towards a better understanding of the so-called Bernstein problem in higher dimensional Heisenberg groups. Indeed, in the sub-Riemannian Heisenberg group $\mathbb{H}^n$, with $n\geq 2$, we show that the only entire hypersurfaces with vanishing horizontal symmetric second fundamental form are hyperplanes. This result relies on a sub-Riemannian characterization of a higher dimensional ruling property, as well as on the study of sub-Riemannian geodesi…

Friday Links 24-10
Two weeks of links, which includes a collection from the xz debacle. I loved reading these, as this is a good combination of spy story and technology postmortem. If you want to read an overview, read the timeline post.
Good podcasts this week: about the Heisenberg principle, and the silencing of climate protesters in the UK.

Friday Links 24-10
Two weeks of links, which includes a collection from the xz debacle. I loved reading these, as this is a good combination of spy story and t...

This https://arxiv.org/abs/2312.17390 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Quantum Hamiltonian Learning for the Fermi-Hubbard Model
This work proposes a protocol for Fermionic Hamiltonian learning. For the Hubbard model defined on a bounded-degree graph, the Heisenberg-limited scaling is achieved while allowing for state preparation and measurement errors. To achieve $ε$-accurate estimation for all parameters, only $\tilde{\mathcal{O}}(ε^{-1})$ total evolution time is needed, and the constant factor is independent of the system size. Moreover, our method only involves simple one or two-site Fermionic manipulations, which …

High temperature series expansions of S = 1/2 Heisenberg spin models: algorithm to include the magnetic field with optimized complexity
Laurent Pierre, Bernard Bernu, Laura Messio
https://arxiv.org/abs/2404.02271

High temperature series expansions of S = 1/2 Heisenberg spin models: algorithm to include the magnetic field with optimized complexity
This work presents an algorithm for calculating high temperature series expansions (HTSE) of Heisenberg spin models with spin $S=1/2$ in the thermodynamic limit. This algorithm accounts for the presence of a magnetic field. The paper begins with a comprehensive introduction to HTSE and then focuses on identifying the bottlenecks that limit the computation of higher order coefficients. HTSE calculations involve two key steps: graph enumeration on the lattice and trace calculations for each graph…

Semisimple Algebras of Vector Fields on $\mathbb{C}^{3}$
Sajid Ali, Hassan Azad, Indranil Biswas, Fazal M. Mahomed, Said Waqas Shah
https://arxiv.org/abs/2404.02847

Semisimple Algebras of Vector Fields on $\mathbb{C}^{3}$
A local classification of semisimple algebras of vector fields on $\mathbb{C}^{3}$ is given, using the canonical forms of the Heisenberg algebra and of $sl(2,\mathbb{C})\times sl(2,\mathbb{C})$.

Exact Evaluation and extrapolation of the divergent expansion for the Heisenberg-Euler Lagrangian II: Non-alternating Case
Christian D. Tica, Eric A. Galapon
https://arxiv.org/abs/2402.14839

Exact Evaluation and extrapolation of the divergent expansion for the Heisenberg-Euler Lagrangian II: Non-alternating Case
We applied the method of finite-part integration [Galapon E.A Proc.R.Soc A 473, 20160567(2017)] to evaluate in closed-form the exact one-loop integral representations of the Heisenberg-Euler Lagrangian from QED for a constant electric field and electric-like self-dual background. We also devise a prescription based on the finite-part integration of the Cauchy principal value integral to sum and extrapolate the non-alternating divergent weak-field expansions of the Heisenberg-Euler Lagrangians t…

Gaussian Formalism: Concrete Realization of Joint Measurement for Heisenberg's Uncertainty Relation for Errors
Kin-ya Oda, Naoya Ogawa
https://arxiv.org/abs/2403.19440

Gaussian Formalism: Concrete Realization of Joint Measurement for Heisenberg's Uncertainty Relation for Errors
We point out that the Gaussian wave-packet formalism can serve as a concrete realization of the joint measurement of position and momentum, which is an essential element in understanding Heisenberg's original philosophy of the uncertainty principle, in line with the universal framework of error, disturbance, and their uncertainty relations developed by Lee and Tsutsui. We show that our joint measurement in the Gaussian phase space, being a Positive Operator-Valued Measure (POVM) measurement, sm…

Heisenberg Soft Hair on Robinson-Trautman Spacetimes
H. Adami, A. Parvizi, M. M. Sheikh-Jabbari, V. Taghiloo
https://arxiv.org/abs/2402.17658 https://

Heisenberg Soft Hair on Robinson-Trautman Spacetimes
We study 4 dimensional $(4d$) gravitational waves (GWs) with compact wavefronts, generalizing Robinson-Trautman (RT) solutions in Einstein gravity with an arbitrary cosmological constant. We construct the most general solution of the GWs in the presence of a causal, timelike, or null boundary when the usual tensor modes are turned off. Our solution space besides the shape and topology of the wavefront which is a generic compact, smooth, and orientable $2d$ surface $Σ$, is specified by a vector…

K-theoretic Heisenberg algebras and permutation-equivariant Gromov--Witten theory
Todor Milanov
https://arxiv.org/abs/2403.14964 https://

K-theoretic Heisenberg algebras and permutation-equivariant Gromov--Witten theory
We found an interesting application of the K-theoretic Heisenberg algebras of Weiqiang Wang to the foundations of permutation equivariant K-theoretic Gromov--Witten theory. We also found an explicit formula for the genus 0 correlators in the permutation equivariant Gromov--Witten theory of the point. In the non-equivariant limit our formula reduces to a well known formula due to Y.P. Lee.

Measure contraction property and curvature-dimension condition on sub-Finsler Heisenberg groups
Samu\"el Borza, Mattia Magnabosco, Tommaso Rossi, Kenshiro Tashiro
https://arxiv.org/abs/2402.14779

Measure contraction property and curvature-dimension condition on sub-Finsler Heisenberg groups
In this paper, we investigate the validity of synthetic curvature-dimension bounds in the sub-Finsler Heisenberg group, equipped with a positive smooth measure. Firstly, we study the measure contraction property, in short $\mathsf{MCP}$, proving that its validity depends on the norm generating the sub-Finsler structure. Indeed, we show that, if it is neither $C^1$ nor strongly convex, the associated Heisenberg group does not satisfy $\mathsf{MCP}(K,N)$ for any pair of parameters $K \in \mathbb{…

Testing gravitational waveforms in full General Relativity
Fabio D'Ambrosio, Francesco Gozzini, Lavinia Heisenberg, Henri Inchausp\'e, David Maibach, Jann Zosso
https://arxiv.org/abs/2402.19397

Testing gravitational waveforms in full General Relativity
We perform a comprehensive analysis of state-of-the-art waveform models, focusing on their predictions concerning kick velocity and inferred gravitational wave memory. In our investigation we assess the accuracy of waveform models using energy-momentum balance laws, which were derived in the framework of full, non-linear General Relativity. The numerical accuracy assessment is performed for precessing as well as non-precessing scenarios for models belonging to the \textit{EOB}, \textit{Phenom},…

Exact Evaluation and extrapolation of the divergent expansion for the Heisenberg-Euler Lagrangian II: Non-alternating Case
Christian D. Tica, Eric A. Galapon
https://arxiv.org/abs/2402.14839

Exact Evaluation and extrapolation of the divergent expansion for the Heisenberg-Euler Lagrangian II: Non-alternating Case
We applied the method of finite-part integration [Galapon E.A Proc.R.Soc A 473, 20160567(2017)] to evaluate in closed-form the exact one-loop integral representations of the Heisenberg-Euler Lagrangian from QED for a constant electric field and electric-like self-dual background. We also devise a prescription based on the finite-part integration of the Cauchy principal value integral to sum and extrapolate the non-alternating divergent weak-field expansions of the Heisenberg-Euler Lagrangians t…

Beyond the random phase approximation for calculating Curie temperatures in ferromagnets: application to Fe, Ni, Co and monolayer CrI3
Varun Rajeev Pavizhakumari, Thorbj{\o}rn Skovhus, Thomas Olsen
https://arxiv.org/abs/2405.00477

Beyond the random phase approximation for calculating Curie temperatures in ferromagnets: application to Fe, Ni, Co and monolayer CrI3
The magnetic properties of solids are typically analyzed in terms of Heisenberg models where the electronic structure is approximated by interacting localized spins. However, even in such models the evaluation of thermodynamic properties constitutes a major challenge and is usually handled by a mean field decoupling scheme. The random phase approximation (RPA) comprises a common approach and is often applied to evaluate critical temperatures although it is well known that the method is only acc…

Nonlinear Heisenberg-Robertson-Schrodinger Uncertainty Principle
K. Mahesh Krishna
https://arxiv.org/abs/2403.17946 https://arxiv.org…

Nonlinear Heisenberg-Robertson-Schrodinger Uncertainty Principle
We derive an uncertainty principle for Lipschitz maps acting on subsets of Banach spaces. We show that this nonlinear uncertainty principle reduces to the Heisenberg-Robertson-Schrodinger uncertainty principle for linear operators acting on Hilbert spaces.

This https://arxiv.org/abs/2404.16713 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Geometry of paraquaternionic contact structures
We introduce the notion of paraquaternionic contact structures (pqc structures), which turns out to be a generalization of the para 3-Sasakian geometry. We derive a distinguished linear connection preserving the pqc structure. Its torsion tensor is expressed explicitly in terms of the structure tensors. We define pqc-Einstein manifolds and show that para 3-Sasakian spaces are precisely pqc manifolds, which are pqc-Einstein. We introduce the paraquaternionic Heisenberg qroup and show that it is …

This https://arxiv.org/abs/2205.04159 has been replaced.
link: https://scholar.google.com/scholar?q=a

Symmetric Stable Processes on Amenable Groups
We show that if $G$ is a countable amenable group, then every stationary non-Gaussian symmetric $α$-stable (S$α$S) process indexed by $G$ is ergodic if and only if it is weakly-mixing, and it is ergodic if and only if its Rosinski minimal spectral representation is null. This extends the results for $\mathbb{Z}^d$, and answers a question of P. Roy on discrete nilpotent groups to the extent of all countable amenable groups. As a result we construct on the Heisenberg group and on many Abelian g…

This https://arxiv.org/abs/2401.07244 has been replaced.
initial toot: https://mastoxiv.page/@arX…

Incremental SWAP Operator for Entanglement Entropy: Application for Exponential Observables in Quantum Monte Carlo Simulation
We propose a new method to efficiently compute the entanglement entropy (EE) of quantum many-body systems. Our approach, called the incremental SWAP operator method , combines the simplicity of the SWAP operator used in projector quantum Monte Carlo simulations with recent advances in precisely computing exponential observables using incremental algorithms. We apply this technique to obtain accurate EE data at reduced computational cost for 1d and 2d antiferromagnetic Heisenberg models with dif…

Parametrically long lifetime of superdiffusion in non-integrable spin chains
Adam J. McRoberts, Roderich Moessner
https://arxiv.org/abs/2402.18662 https://…

Parametrically long lifetime of superdiffusion in non-integrable spin chains
Superdiffusion is surprisingly easily observed even in systems without the integrability underpinning this phenomenon. Indeed, the classical Heisenberg chain -- one of the simplest many-body systems, and firmly believed to be non-integrable -- evinces a long-lived regime of anomalous, superdiffusive spin dynamics at finite temperature. Similarly, superdiffusion persists for long timescales, even at high temperature, for small perturbations around a related integrable model. Eventually, however,…

On the Cohomology of Restricted Heisenberg Lie Algebras
Tyler J. Evans, Alice Fialowski, Yong Yang
https://arxiv.org/abs/2402.14249 https://

On the Cohomology of Restricted Heisenberg Lie Algebras
We show that the Heisenberg Lie algebras over an algebraically closed field $\mathbb{F}$ of characteristic $p>0$ admit a family of restricted Lie algebras. We use the ordinary 1- and 2-cohomology spaces with trivial coefficients to compute the restricted 1- and 2-cohomology spaces of these restricted Heisenberg Lie algebras. We describe the restricted 1-dimensional central extensions, including explicit formulas for the Lie brackets and $\cdot^{[p]}$-operators.

This https://arxiv.org/abs/2311.13211 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Fractional Caffarelli-Kohn-Nirenberg type inequalities on the Heisenberg group
The aim of this work is to establish some cases of the Caffarelli-Kohn-Nirenberg inequalities on the Heisenberg group for the fractional Sobolev spaces. Here we work with the fractional Sobolev spaces as given by Adimurthi and Mallick in [1]. Our inequalities also give an improvement on the range of indices for the Hardy type inequality established in [1].

The Folland-Stein spectrum of some Heisenberg Bieberbach manifold
Yoshiaki Suzuki
https://arxiv.org/abs/2402.15093 https://arxiv.org/…

The Folland-Stein spectrum of some Heisenberg Bieberbach manifold
We study the eigenvalues and eigenfunctions of the Folland-Stein operator $\mathscr{L}_α$ on some example of 3-dimensional Heisenberg Bieberbach manifolds, that is, compact quotients $Γ\backslash\mathbb{H}$ of the Heisenberg group $\mathbb{H}$ by a discrete torsion-free subgroup $Γ$ of $\mathbb{H}\rtimes U(1)$.

A diverse set of two-qubit gates for spin qubits in semiconductor quantum dots
Ming Ni, Rong-Long Ma, Zhen-Zhen Kong, Ning Chu, Sheng-Kai Zhu, Chu Wang, Ao-Ran Li, Wei-Zhu Liao, Gang Cao, Gui-Lei Wang, Guang-Can Guo, Xuedong Hu, Hai-Ou Li, Guo-Ping Guo
https://arxiv.org/abs/2404.18689

A diverse set of two-qubit gates for spin qubits in semiconductor quantum dots
To realize large-scale quantum information processes, an ideal scheme for two-qubit operations should enable diverse operations with given hardware and physical interaction. However, for spin qubits in semiconductor quantum dots, the common two-qubit operations, including CPhase gates, SWAP gates, and CROT gates, are realized with distinct parameter regions and control waveforms, posing challenges for their simultaneous implementation. Here, taking advantage of the inherent Heisenberg interacti…

Non-stabilizerness versus entanglement in matrix product states
M. Frau, P. S. Tarabunga, M. Collura, M. Dalmonte, E. Tirrito
https://arxiv.org/abs/2404.18768

Non-stabilizerness versus entanglement in matrix product states
In this paper, we investigate the relationship between entanglement and non-stabilizerness (also known as magic) in matrix product states (MPSs). We study the relation between magic and the bond dimension used to approximate the ground state of a many-body system in two different contexts: full state of magic and mutual magic (the non-stabilizer analogue of mutual information, thus free of boundary effects) of spin-1 anisotropic Heisenberg chains. Our results indicate that obtaining converged r…

Analytical solutions of symmetric isotropic spin clusters
Shadan Ghassemi Tabrizi, Thomas D. K\"uhne
https://arxiv.org/abs/2405.00214 https://<…

Analytical solutions of symmetric isotropic spin clusters
Spin models like the Heisenberg Hamiltonian effectively describe the interactions of open-shell transition-metal ions on a lattice and can account for various properties of magnetic solids and molecules. Numerical methods are usually required to find exact or approximate eigenstates, but for small clusters with spatial symmetry, analytical solutions exist, and a few Heisenberg systems have been solved in closed form. This paper presents a simple, generally applicable approach to analytically so…

Many-body localization properties of fully frustrated Heisenberg spin-1/2 ladder model with next-nearest-neighbor interaction
Jiameng Hong, Taotao Hu
https://arxiv.org/abs/2402.11272

Many-body localization properties of fully frustrated Heisenberg spin-1/2 ladder model with next-nearest-neighbor interaction
Many-body localization (MBL) is an intriguing physical phenomenon that arises from the interplay of interaction and disorder, allowing quantum systems to prevent thermalization. In this study, we investigate the MBL properties of the fully frustrated Heisenberg spin-1/2 ladder model with next-nearest-neighbor hopping interaction along the leg direction and compare it with the Heisenberg spin-1/2 single-chain model with next-nearest-neighbor hopping interaction. We explore the MBL transition usi…

Hilbert transforms and maximal functions along flat curves on the Heisenberg group
Lingxiao Zhang
https://arxiv.org/abs/2402.10653 https://

Hilbert transforms and maximal functions along flat curves on the Heisenberg group
We establish the $L^p$ boundedness of Hilbert transforms and maximal functions along flat curves in the Heisenberg group. This generalizes the $\mathbb{R}^n$ result by Carbery, Christ, Vance, Wainger, and Watson. What is new about our result compared to the Heisenberg group generalization by Carbery, Wainger, and Wright is that we allow all three components of the curves to vary independently, we keep the original form of the conditions required in the $\mathbb{R}^n$ case, and our method is lik…

Optical properties of Euler-Heisenberg black hole in the Cold Dark Matter Halo
Lei You, Rui-bo Wang, Shi-Jie Ma, Jian-Bo Deng, Xian-Ru Hu
https://arxiv.org/abs/2403.12840

Optical properties of Euler-Heisenberg black hole in the Cold Dark Matter Halo
The optical properties of Euler-Heisenberg (EH) black hole (BH) surrounded by Cold Dark Matter (CDM) halo are investigated. By changing BH's parameters, we found that the radius of horizon r_{h} and radius of photon sphere r_{ph} will transparently increase as CDM halo parameters R and ρincrease. To show the influence of CDM halo on the BH's optical characteristics, we took two sets of R and ρwith prominent differences and plot the first four orders of images for thin accretion disk with diff…

Nonlinear Heisenberg-Robertson-Schrodinger Uncertainty Principle
K. Mahesh Krishna
https://arxiv.org/abs/2403.17946 https://arxiv.org…

Nonlinear Heisenberg-Robertson-Schrodinger Uncertainty Principle
We derive an uncertainty principle for Lipschitz maps acting on subsets of Banach spaces. We show that this nonlinear uncertainty principle reduces to the Heisenberg-Robertson-Schrodinger uncertainty principle for linear operators acting on Hilbert spaces.

Submanifolds with boundary and Stokes' Theorem in Heisenberg groups
Marco Di Marco, Antoine Julia, Sebastiano Nicolussi Golo, Davide Vittone
https://arxiv.org/abs/2403.18675 <…

Submanifolds with boundary and Stokes' Theorem in Heisenberg groups
We introduce and study the notion of $C^1_\mathbb{H}$-regular submanifold with boundary in sub-Riemannian Heisenberg groups. As an application, we prove a version of Stokes' Theorem for $C^1_\mathbb{H}$-regular submanifolds with boundary that takes into account Rumin's complex of differential forms in Heisenberg groups.

Photon frequency variation in non-linear electro-magnetism
Alessandro D. A. M. Spallicci, Abedennour Dib, Jos\'e A. Helay\"el-Neto
https://arxiv.org/abs/2404.18951

Photon frequency variation in non-linear electro-magnetism
We set a generalised non-linear Lagrangian, encompassing Born-Infeld and Heisenberg-Euler theories among others. The Lagrangian reduces to the Maxwell Lagrangian at lowest order. The field is composed by a propagating light-wave in an electro-magnetic background. The wave exhibits energy variation when the background is space-time dependent. In the photon description, this implies a red or a blue shift, like what we obtained in massive theories, as the de Broglie-Proca or effective mass theorie…

A Generic Nonlinear Evolution Equation of Magnetic Type II. Particular Solutions
T. Valchev
https://arxiv.org/abs/2403.18165 https://…

A Generic Nonlinear Evolution Equation of Magnetic Type II. Particular Solutions
We consider a matrix nonlinear partial differential equation that generalizes Heisenberg ferromagnet equation. This generalized Heisenberg ferromagnet equation is completely integrable with a linear bundle Lax pair related to the pseudo-unitary algebra. This allows us to explicitly derive particular solutions by using dressing technique. We shall discuss two classes of solutions over constant background: soliton-like solutions and quasi-rational solutions. Both classes have their analogues in t…

Tunable topological phases in nanographene-based spin-1/2 alternating-exchange Heisenberg chains
Chenxiao Zhao, Gon\c{c}alo Catarina, Jin-Jiang Zhang, Jo\~ao C. G. Henriques, Lin Yang, Ji Ma, Xinliang Feng, Oliver Gr\"oning, Pascal Ruffieux, Joaqu\'in Fern\'andez-Rossier, Roman Fasel
https://arxiv.org/abs/2402.13590…

Tunable topological phases in nanographene-based spin-1/2 alternating-exchange Heisenberg chains
Unlocking the potential of topological order within many-body spin systems has long been a central pursuit in the realm of quantum materials. Despite extensive efforts, the quest for a versatile platform enabling site-selective spin manipulation, essential for tuning and probing diverse topological phases, has persisted. Here, we utilize on-surface synthesis to construct spin-1/2 alternating-exchange Heisenberg (AH) chains[1] with antiferromagnetic couplings $J_1$ and $J_2$ by covalently linkin…

The universal Lipschitz path space of the Heisenberg group $\mathbb{H}^1$
Daniel Perry
https://arxiv.org/abs/2402.10420 https://arxiv…

The universal Lipschitz path space of the Heisenberg group $\mathbb{H}^1$
The goal of this paper is to define and inspect a metric version of the universal path space and study its application to purely 2-unrectifiable spaces, in particular the Heisenberg group $\mathbb{H}^1$. The construction of the universal Lipschitz path space, as the metric version is called, echoes the construction of the universal cover for path-connected, locally path-connected, and semilocally simply connected spaces. We prove that the universal Lipschitz path space of a purely 2-unrectifiab…

Comment on "All-Loop Result for the Strong Magnetic Field Limit of the Heisenberg-Euler Effective Lagrangian"
Stefan Evans, Johann Rafelski
https://arxiv.org/abs/2403.09745

Comment on "All-Loop Result for the Strong Magnetic Field Limit of the Heisenberg-Euler Effective Lagrangian"
We offer a 2nd look at the recently claimed improvement of Euler-Heisenberg-Schwinger (EHS) action [PRL \textbf{122} (2019) no.21, 211602 and post-publication correction]: We demonstrate a difference to the claimed concordance with the Schwinger-Dyson series starting at the two-loop level.

This https://arxiv.org/abs/2310.17883 has been replaced.
initial toot: https://mastoxiv.page/@arX…

Ground state of the staggered Heisenberg-$Γ$ honeycomb model in a magnetic field
We study the ground state properties of the $S=\frac{1}{2}$ staggered Heisenberg-$Γ$ honeycomb model under a magnetic field based on analytical and numerical methods. Our calculations show that the conventional zigzag and stripy phases are favored because of the staggered Heisenberg interaction away from the pure $Γ$ limit. In our classical analysis, we find that the field induces a series of competing magnetic phases with relatively large unit cells in the region sandwiched between the two m…

This https://arxiv.org/abs/2311.17257 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Graded pseudo-traces for strongly interlocked modules for a vertex operator algebra and applications
We define the notion of strongly interlocked for indecomposable generalized modules for a vertex operator algebra, and show that the notion of graded pseudo-trace is well defined for modules which satisfy this property. We prove that the graded pseudo-trace is a symmetric linear operator that satisfies the logarithmic derivative property. As an application, we prove that all the indecomposable reducible generalized modules for the rank one Heisenberg (one free boson) vertex operator algebras ar…

This https://arxiv.org/abs/2403.00069 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Learning interacting fermionic Hamiltonians at the Heisenberg limit
Efficiently learning an unknown Hamiltonian given access to its dynamics is a problem of interest for quantum metrology, many-body physics and machine learning. A fundamental question is whether learning can be performed at the Heisenberg limit, where the Hamiltonian evolution time scales inversely with the error, $\varepsilon$, in the reconstructed parameters. The Heisenberg limit has previously been shown to be achievable for certain classes of qubit and bosonic Hamiltonians. Most recently, a…

Anti-Instability of Complex Ghost
Jisuke Kubo, Taichiro Kugo
https://arxiv.org/abs/2402.15956 https://arxiv.org/pdf/2402.15956…

Anti-Instability of Complex Ghost
We argue that Lee-Wick's complex ghost appearing in any higher derivative theory is stable and its asymptotic field exists. It may be more appropriate to call it ``anti-unstable" in the sense that, the more the ghost `decays' into lighter ordinary particles, the larger the probability the ghost remains as itself becomes. This is explicitly shown by analyzing the two-point functions of the ghost Heisenberg field which is obtained as an exact result in the $N\rightarrow\infty$ limit in a massive …

This https://arxiv.org/abs/2308.01153 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Struwe's Global Compactness and energy approximation of the critical Sobolev embedding in the Heisenberg group
We investigate some of the effects of the lack of compactness in the critical Folland-Stein-Sobolev embedding in very general (possible non-smooth) domains, by proving via De Giorgi's $Γ$-convergence techniques that optimal functions for a natural subcritical approximations of the Sobolev quotient concentrate energy at one point. In the second part of the paper, we try to restore the compactness by extending the celebrated Global Compactness result to the Heisenberg group via a completely diff…

This https://arxiv.org/abs/2308.04959 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_…

Rayleigh and Raman scattering cross-sections and phase matrices of the ground-state hydrogen atom, and their astrophysical implications
We present explicit expressions for Rayleigh and Raman scattering cross-sections and phase matrices of the ground $1s$ state hydrogen atom based on the Kramers-Heisenberg dispersion formula. The Rayleigh scattering leaves the hydrogen atom in the ground-state while the Raman scattering leaves the hydrogen atom in either $ns$ ($n\geq2$; $s$-branch) or $nd$ ($n\geq3$; $d$-branch) excited state, and the Raman scattering converts incident ultraviolet (UV) photons around the Lyman resonance lines in…

This https://arxiv.org/abs/2307.14533 has been replaced.
initial toot: https://mastoxiv.page/@a…

Electromagnon excitations in high temperature superconducting states
In this article, we discover a fundamental excitation called electromagnon in the cuprate superconducting states. Doped holes render local inversion asymmetry which produces hidden Rashba spin-orbit coupling in copper-oxide plane. Rashba effect leads to Dzyaloshinskii-Moriya (DM) interaction between neighboring spins, which establishes a general spin Hamitonian combined with Heisenberg exchange interaction. The physical origin of spin fluctuations has been revealed from Rashba-induced DM term. …

This https://arxiv.org/abs/2402.02990 has been replaced.
link: https://scholar.google.com/scholar?q=a

Poisson-Lie analogues of spin Sutherland models revisited
Some generalizations of spin Sutherland models descend from `master integrable systems' living on Heisenberg doubles of compact semisimple Lie groups. The master systems represent Poisson--Lie counterparts of the systems of free motion modeled on the respective cotangent bundles and their reduction relies on taking quotient with respect to a suitable conjugation action of the compact Lie group. We present an enhanced exposition of the reductions and prove rigorously for the first time that the …

Bound-state confinement after trap-expansion dynamics in integrable systems
Leonardo Biagetti, Vincenzo Alba
https://arxiv.org/abs/2402.17623 https://

Bound-state confinement after trap-expansion dynamics in integrable systems
Integrable systems possess stable families of quasiparticles, which are composite objects (bound states) of elementary excitations. Motivated by recent quantum computer experiments, we investigate bound-state transport in the spin-$1/2$ anisotropic Heisenberg chain ($XXZ$ chain). Specifically, we consider the sudden vacuum expansion of a finite region $A$ prepared in a non-equilibrium state. In the hydrodynamic regime, if interactions are strong enough, bound states remain confined in the initi…

This https://arxiv.org/abs/2302.08306 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Isotopisms of nilpotent Leibniz algebras and Lie racks
In this paper we study the isotopism classes of two-step nilpotent algebras. We show that every nilpotent Leibniz algebra $\mathfrak{g}$ with $\operatorname{dim}[\mathfrak{g},\mathfrak{g}]=1$ is isotopic to the Heisenberg Lie algebra or to the Heisenberg algebra $\mathfrak{l}_{2n+1}^{J_1}$, where $J_1$ is the $n \times n$ Jordan block of eigenvalue 1. We also prove that two such algebras are isotopic if and only if the Lie racks integrating them are isotopic. This gives the classification of Li…

A Generic Nonlinear Evolution Equation of Magnetic Type II. Particular Solutions
T. Valchev
https://arxiv.org/abs/2403.18165 https://…

A Generic Nonlinear Evolution Equation of Magnetic Type II. Particular Solutions
We consider a matrix nonlinear partial differential equation that generalizes Heisenberg ferromagnet equation. This generalized Heisenberg ferromagnet equation is completely integrable with a linear bundle Lax pair related to the pseudo-unitary algebra. This allows us to explicitly derive particular solutions by using dressing technique. We shall discuss two classes of solutions over constant background: soliton-like solutions and quasi-rational solutions. Both classes have their analogues in t…

Exploring magnetic anisotropy in bcc-structured ferromagnetic thin films with three spin layers using the fourth order perturbed Heisenberg Hamiltonian
M. S. M. Farhan
https://arxiv.org/abs/2403.13817

Exploring magnetic anisotropy in bcc-structured ferromagnetic thin films with three spin layers using the fourth order perturbed Heisenberg Hamiltonian
This study investigates into the analysis of ferromagnetic thin films with a body centered cubic lattice and three spin layers, utilizing the solution of the fourth-order perturbed Heisenberg Hamiltonian equation with seven magnetic energy parameters. Spin-exchange interaction, magnetic dipole interaction, second-order magnetic anisotropy,fourth-order magnetic anisotropy, applied magnetic field, demagnetization energy, and stress-induced anisotropy were all taken into account. According to 3D p…

This https://arxiv.org/abs/2308.08178 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Minimal null scrolls in the three-dimensional Heisenberg group
In the three-dimensional Heisenberg group equipped with a certain left invariant Lorentzian metric, timelike minimal surfaces which have the Abresch-Rosenberg differentials with vanishing multiplication of the coefficient function and its para-complex conjugate are characterized as the surfaces defined by the multiplication of null curves and affine null lines. Moreover, the constructions of these surfaces with prescribed curvatures of null curves or prescribed null lines are given.

Anti-Instability of Complex Ghost
Jisuke Kubo, Taichiro Kugo
https://arxiv.org/abs/2402.15956 https://arxiv.org/pdf/2402.15956…

Anti-Instability of Complex Ghost
We argue that Lee-Wick's complex ghost appearing in any higher derivative theory is stable and its asymptotic field exists. It may be more appropriate to call it ``anti-unstable" in the sense that, the more the ghost `decays' into lighter ordinary particles, the larger the probability the ghost remains as itself becomes. This is explicitly shown by analyzing the two-point functions of the ghost Heisenberg field which is obtained as an exact result in the $N\rightarrow\infty$ limit in a massive …

Quiver Heisenberg algebras: a cubic analogue of preprojective algebras
Martin Herschend, Hiroyuki Minamoto
https://arxiv.org/abs/2402.08162 https://…

Quiver Heisenberg algebras: a cubic analogue of preprojective algebras
In this paper we study a certain class of central extensions of preprojective algebras of quivers under the name quiver Heisenberg algebras (QHA). There are several classes of algebras introduced before by different researchers from different view points, which have the QHA as a special case. While these have mainly been studied in characteristic zero, we also study the case of positive characteristic. Our results show that the QHA is closely related to the representation theory of the correspo…

This https://arxiv.org/abs/2402.03572 has been replaced.
link: https://scholar.google.com/scholar?q=a

Entanglement-enhanced quantum metrology: from standard quantum limit to Heisenberg limit
Entanglement-enhanced quantum metrology explores the utilization of quantum entanglement to enhance measurement precision. When particles in a probe are prepared into a quantum entangled state, they collectively accumulate information about the physical quantity to be measured, leading to an improvement in measurement precision beyond the standard quantum limit and approaching the Heisenberg limit. The rapid advancement of techniques for quantum manipulation and detection has enabled the genera…

On Quasi-Locality and Decay of Correlations for Long-Range Models of Open Quantum Spin Systems
Eric B. Roon, Robert Sims
https://arxiv.org/abs/2404.17577 h…

On Quasi-Locality and Decay of Correlations for Long-Range Models of Open Quantum Spin Systems
We consider models of open quantum spin systems with irreversible dynamics and show that general quasi-locality results for long-range models, e.g. as proven for the Heisenberg dynamics associated to quantum systems in [27], naturally extend to this setting. Given these bounds, we provide two applications. First, we use these results to obtain estimates on a strictly local approximation of these finite-volume, irreversible dynamics. Next, we show how these bounds can be used to estimate correla…

Enhanced pair-density-wave vertices in a bilayer Hubbard model at half-filling
Fangze Liu, Xu-Xin Huang, Edwin W. Huang, Brian Moritz, Thomas P. Devereaux
https://arxiv.org/abs/2404.01389

Enhanced pair-density-wave vertices in a bilayer Hubbard model at half-filling
Motivated by the pair-density-wave (PDW) state found in the one-dimensional Kondo-Heisenberg chain, we report on a determinant quantum Monte Carlo DQMC study of pair-fields for a two- dimensional half-filled Hubbard layer coupled to an itinerant, non-interacting layer with one electron per site. In a specific range of interlayer hopping, the pairing vertex associated with PDW order becomes more attractive than that for uniform d-wave pairing, although both remain subdominant to the leading anti…

Non-Markovian maximal couplings and a vertical reflection principle on a class of sub-Riemannian manifolds
Liangbing Luo, Robert W. Neel
https://arxiv.org/abs/2402.13976

Non-Markovian maximal couplings and a vertical reflection principle on a class of sub-Riemannian manifolds
We develop non-Markovian, non-co-adapted couplings for sub-Riemannian Brownian motions in various sub-Riemannian manifolds, namely the three-dimensional Heisenberg group, higher-dimensional non-isotropic Heisenberg groups, SL(2,R) and its universal cover, and SU(2,C). Our primary focus is on the situation when the processes start from two points on the same vertical fiber, since in general co-adapted couplings cannot give the sharp rate for the coupling time in this case. Then for general point…

Euler-Heisenberg Black Holes in Einsteinian Cubic Gravity
Gustavo Gutierrez-Cano, Gustavo Niz
https://arxiv.org/abs/2402.06867 https://

Euler-Heisenberg Black Holes in Einsteinian Cubic Gravity
We explore black hole solutions and some of its physical properties in Einstein's theory in 4D, modified by a cubic gravity term and in the presence of non-linear electrodynamics. In the context of Effective Field Theories (EFT) and under certain assumptions, these curvature and non-linear electromagnetic terms represent the first corrections to the Einstein-Maxwell theory. We obtain static and spherically symmetric generalizations to the asymptotically flat Reissner-Nordström metric using per…

Convolution operators and variable Hardy spaces on the Heisenberg group
Pablo Rocha
https://arxiv.org/abs/2403.11467 https://arxiv.or…

Convolution operators and variable Hardy spaces on the Heisenberg group
Let $\mathbb{H}^{n}$ be the Heisenberg group. For $0 \leq α< Q=2n+2$ and $N \in \mathbb{N}$ we consider exponent functions $p(\cdot) : \mathbb{H}^{n} \to (0, +\infty)$, which satisfies Hölder conditions, such that $\frac{Q}{Q+N} < p_{-} \leq p(\cdot) \leq p_{+} < \frac{Q}α$. In this article we prove the $H^{p(\cdot)}(\mathbb{H}^{n}) \to L^{q(\cdot)}(\mathbb{H}^{n})$ and $H^{p(\cdot)}(\mathbb{H}^{n}) \to H^{q(\cdot)}(\mathbb{H}^{n})$ boundedness of convolution operators with kernels of type $…

This https://arxiv.org/abs/2311.16428 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Jerison-Lee identity and Semi-linear subelliptic equation on CR manifold
In the study of the extremal for Sobolev inequality on the Heisenberg group and the Cauchy-Riemann(CR) Yamabe problem, Jerison-Lee found a three-dimensional family of differential identities for critical exponent subelliptic equation on Heisenberg group $\mathbb H^n$ by using the computer in [11]. They wanted to know whether there is a theoretical framework that would predict the existence and the structure of such formulae. With the help of dimensional conservation and invariant tensors, we ca…

This https://arxiv.org/abs/2212.09511 has been replaced.
link: https://scholar.google.com/scholar?q=a

Logarithmic negativity of the 1D antiferromagnetic spin-1 Heisenberg model with single-ion anisotropy
We study the 1D antiferromagnetic spin-1 Heisenberg XXX model with external magnetic field B and single-ion anisotropy D on finite chains. We determine the nearest and non-nearest neighbor logarithmic entanglement LN. Our main result is the disappearance of LN both for nearest and non-nearest neighbor (next-nearest and next-next-nearest) sites at zero temperature and for low temperature states. Such disappearance occurs at a critical value of B and D. The resulting phase diagram for the behavio…

This https://arxiv.org/abs/2401.03616 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

An improved Quantum Max Cut approximation via matching
Finding a high (or low) energy state of a given quantum Hamiltonian is a potential area to gain a provable and practical quantum advantage. A line of recent studies focuses on Quantum Max Cut, where one is asked to find a high energy state of a given antiferromagnetic Heisenberg Hamiltonian. In this work, we present a classical approximation algorithm for Quantum Max Cut that achieves an approximation ratio of 0.584 given a generic input, and a ratio of 0.595 given a triangle-free input, outper…

The magnetization process of classical Heisenberg magnets with non-coplanar cuboc ground states
Johannes Richter, Heinz-J\"urgen Schmidt, J\"urgen Schnack
https://arxiv.org/abs/2404.16682

The magnetization process of classical Heisenberg magnets with non-coplanar cuboc ground states
We consider a classical Heisenberg model on the kagomé and the square kagomé lattice, where at zero magnetic field non-coplanar cuboctahedral ground states with twelve sublattices exist if suitable exchange couplings are introduced between the other neighbors. Such 'cuboc ground states' are remarkable because they allow for chiral ordering. For these models, we discuss the magnetization process in an applied magnetic field $H$ by both numerical and analytical methods. We find some universal p…

This https://arxiv.org/abs/2310.08199 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Exact evaluation and extrapolation of the divergent expansion for the Heisenberg-Euler Lagrangian I: Alternating Case
We applied the method of finite-part integration [Galapon E.A Proc.R.Soc A 473, 20160567(2017)] to evaluate in closed-form the exact one-loop integral representations of the Heisenberg-Euler Lagrangian from QED for a constant magnetic field and magnetic-like self-dual background. We also devise a prescription based on the finite-part integration of a generalized Stieltjes integral to sum and extrapolate to the strong-field regime the alternating divergent weak-field expansions of the Heisenberg…

This https://arxiv.org/abs/2402.03711 has been replaced.
link: https://scholar.google.com/scholar?q=a

Evidence that the AT transition disappears below six dimensions
One of the key predictions of Parisi's broken replica symmetry theory of spin glasses is the existence of a phase transition in an applied field to a state with broken replica symmetry. This transition takes place at the de Almeida-Thouless (AT) line in the $h-T$ plane. We have studied this line in the power-law diluted Heisenberg spin glass in which the probability that two spins separated by a distance $r$ interact with each other falls as $1/r^{2σ}$. In the presence of a random vector-field…

This https://arxiv.org/abs/2212.09511 has been replaced.
link: https://scholar.google.com/scholar?q=a

Logarithmic negativity of the 1D antiferromagnetic spin-1 Heisenberg model with single-ion anisotropy
We study the 1D antiferromagnetic spin-1 Heisenberg XXX model with external magnetic field B and single-ion anisotropy D on finite chains. We determine the nearest and non-nearest neighbor logarithmic entanglement LN. Our main result is the disappearance of LN both for nearest and non-nearest neighbor (next-nearest and next-next-nearest) sites at zero temperature and for low temperature states. Such disappearance occurs at a critical value of B and D. The resulting phase diagram for the behavio…

Local control on quaternionic Heisenberg group of dimension $7$
Jan Eisner, Lenka Zalabov\'a
https://arxiv.org/abs/2404.08953 https://

Local control on quaternionic Heisenberg group of dimension $7$
We describe the quaternionic Heisenberg group in the dimension $7$ as a matrix group. We study the local control of a compatible left-invariant control system. We describe the impact of symmetries of the corresponding sub-Riemannian structure on the optimality of geodesics.

This https://arxiv.org/abs/2402.06867 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Euler-Heisenberg Black Holes in Einsteinian Cubic Gravity
We explore black hole solutions and some of its physical properties in Einstein's theory in 4D, modified by a cubic gravity term and in the presence of non-linear electrodynamics. In the context of Effective Field Theories (EFT) and under certain assumptions, these curvature and non-linear electromagnetic terms represent the first corrections to the Einstein-Maxwell theory. We obtain static and spherically symmetric generalizations to the asymptotically flat Reissner-Nordström metric using per…

This https://arxiv.org/abs/2209.08080 has been replaced.
link: https://scholar.google.com/scholar?q=a

Is the relaxation dynamics of spatially disordered quantum spin systems universal?
A major goal toward understanding far-from-equilibrium dynamics of quantum many-body systems consists in finding indications of universality in the sense that the dynamics no longer depends on microscopic details of the system. We realize a large range of many-body spin systems on a Rydberg atom quantum simulator by choosing appropriate Rydberg state combinations. We use this platform to compare the magnetization relaxation dynamics of disordered Heisenberg XX-, XXZ- and Ising Hamiltonians in a…

Hilbert space representation for quasi-Hermitian position-deformed Heisenberg algebra and Path integral formulation
Thomas Katsekpor, Lat\'evi M. Lawson, Prince K. Osei, Ibrahim Nonkan\'e
https://arxiv.org/abs/2404.07082

Hilbert space representation for quasi-Hermitian position-deformed Heisenberg algebra and Path integral formulation
Position deformation of a Heisenberg algebra and Hilbert space representation of both maximal length and minimal momentum uncertainties may lead to loss of Hermiticity of some operators that generate this algebra. Consequently, the Hamiltonian operator constructed from these operators are also not Hermitian. In the present paper, with an appropriate positive-definite Dyson map, we establish the Hermiticity of these operators by means of a quasi-similarity transformation. We then construct Hilbe…

This https://arxiv.org/abs/2402.07980 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Lanczos spectrum for random operator growth
Krylov methods have reappeared recently, connecting physically sensible notions of complexity with quantum chaos and quantum gravity. In these developments, the Hamiltonian and the Liouvillian are tridiagonalized so that Schrodinger/Heisenberg time evolution is expressed in the Krylov basis. In the context of Schrodinger evolution, this tridiagonalization has been carried out in Random Matrix Theory. We extend these developments to Heisenberg time evolution, describing how the Liouvillian can b…

Hardy type inequalities on manifolds with nonnegative Ricci curvature
Yuxin Dong, Hezi Lin, Lingen Lu
https://arxiv.org/abs/2402.17253 https://

Hardy type inequalities on manifolds with nonnegative Ricci curvature
We prove the Hardy inequality, Heisenberg-Pauli-Weyl inequality, Hardy-Sobolev inequality, and Caffarelli-Kohn-Nirenberg (CKN) inequality on manifolds with nonnegative Ricci curvature and Euclidean volume growth, of dimension n>=3.

This https://arxiv.org/abs/2310.08199 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Exact evaluation and extrapolation of the divergent expansion for the Heisenberg-Euler Lagrangian I: Alternating Case
We applied the method of finite-part integration [Galapon E.A Proc.R.Soc A 473, 20160567(2017)] to evaluate in closed-form the exact one-loop integral representations of the Heisenberg-Euler Lagrangian from QED for a constant magnetic field and magnetic-like self-dual background. We also devise a prescription based on the finite-part integration of a generalized Stieltjes integral to sum and extrapolate to the strong-field regime the alternating divergent weak-field expansions of the Heisenberg…

Kitaev-Heisenberg cobaltates: Coulomb exchange as leading nearest-neighbor interaction mechanism
Pritam Bhattacharyya, Thorben Petersen, Satoshi Nishimoto, Liviu Hozoi
https://arxiv.org/abs/2404.12742

Kitaev-Heisenberg cobaltates: Coulomb exchange as leading nearest-neighbor interaction mechanism
A range of honeycomb Co oxide compounds has been proposed and investigated in the search for a topological Kitaev spin liquid. Analyzing the quantum chemistry of interacting magnetic moments in Na$_3$Co$_2$SbO$_6$, a representative $LS$-coupled $t_{2g}^5e_g^2$ magnet, we find that the Kitaev and off-diagonal $Γ$ interactions are sizable and antiferromagnetic but still weaker than the Heisenberg contribution. Except $Γ$', all nearest-neighbor couplings are mainly determined by Coulomb exchange…

This https://arxiv.org/abs/2403.05954 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Unlocking Heisenberg Sensitivity with Sequential Weak Measurement Preparation
We propose a state preparation protocol based on sequential measurements of a central spin coupled with a spin ensemble, and investigate the usefulness of the generated multi-spin states for quantum enhanced metrology. Our protocol is shown to generate highly entangled spin states, devoid of the necessity for non-linear spin interactions. The metrological sensitivity of the resulting state surpasses the standard quantum limit, reaching the Heisenberg limit under symmetric coupling strength cond…

On the lattice model of the Weil representation
Chun-Hui Wang
https://arxiv.org/abs/2404.03983 https://arxiv.org/pdf/2404.03983

On the lattice model of the Weil representation
Let F be a local field. In the case of F being the real field, Pierre Cartier constructed Heisenberg-Weil representations of a Heisenberg group in families using non-self-dual lattices. This result was later reformulated by Jae-Hyun Yang in another paper. We extend this family of representations to a representation of a Jacobi subgroup by incorporating a rational Metaplectic group. In the case of F being a non-archimedean local field of odd residual characteristic or a finite unramified extensi…

Absence of local conserved quantity in the Heisenberg model with next-nearest-neighbor interaction
Naoto Shiraishi
https://arxiv.org/abs/2403.04522 https:/…

Absence of local conserved quantity in the Heisenberg model with next-nearest-neighbor interaction
We rigorously prove that the Heisenberg chain with next-nearest-neighbor interaction, which is anticipated to be non-integrable, is indeed non-integrable in the sense that this system has no nontrivial local conserved quantity. Our result covers two important models, the Majundhar-Ghosh model and the Shastry-Sutherland model, as special cases. These models are shown to be non-integrable while have some solvable energy eigenstates.

This https://arxiv.org/abs/2401.01986 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Generation of complete graph states in a spin-$1/2$ Heisenberg chain with a globally optimized magnetic field
Graph states possess significant practical value in measurement-based quantum computation, with complete graph states that exhibit exceptional performance in quantum metrology. In this work, we introduce a method for generating multiparticle complete graph states using a spin-$1/2$ Heisenberg $XX$ chain subjected to a time-varying magnetic field, which applies to a wide range of systems. Our scheme relies exclusively on nearest-neighbor interactions between atoms, with real-time magnetic field …

This https://arxiv.org/abs/2401.06565 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Semilinear damped wave equations on the Heisenberg group with initial data from Sobolev spaces of negative order
In this paper, we focus on studying the Cauchy problem for semilinear damped wave equations involving the sub-Laplacian $\mathcal{L}$ on the Heisenberg group $\mathbb{H}^n$ with power type nonlinearity $|u|^p$ and initial data taken from Sobolev spaces of negative order homogeneous Sobolev space $\dot H^{-γ}_{\mathcal{L}}(\mathbb{H}^n), γ>0$, on $\mathbb{H}^n$. In particular, in the framework of Sobolev spaces of negative order, we prove that the critical exponent is the exponent $p…

Integrability of the sub-Riemannian geodesic flow of the left-invariant metric on the Heisenberg group
Milan Pavlovic, Tijana Sukilovic
https://arxiv.org/abs/2404.06586

Integrability of the sub-Riemannian geodesic flow of the left-invariant metric on the Heisenberg group
In this paper, we study two different classes of normal geodesic flows corresponding to the left-invariant sub-Riemannian metric on the $(2n+1)$-dimensional Heisenberg group. The first class corresponds to the left-invariant distribution, while the second corresponds to the right-invariant one. We prove that corresponding Hamiltonian L-L and L-R systems are completely integrable.

This https://arxiv.org/abs/2401.12505 has been replaced.
initial toot: https://mastoxiv.page/@arX…

Topological magnons in a non-coplanar magnetic order on the triangular lattice
The bond-dependent Kitaev interaction $K$ is familiar in the effective spin model of transition metal compounds with octahedral ligands. In this work, we find a peculiar non-coplanar magnetic order can be formed with the help of $K$ and next-nearest neighbor Heisenberg coupling $J_2$ on the triangular lattice. It can be seen as a miniature version of skyrmion crystal, since it has nine spins and an integer topological number in a magnetic unit cell. The magnon excitations in such an order are s…

This https://arxiv.org/abs/2402.17658 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Heisenberg Soft Hair on Robinson-Trautman Spacetimes
We study 4 dimensional $(4d$) gravitational waves (GWs) with compact wavefronts, generalizing Robinson-Trautman (RT) solutions in Einstein gravity with an arbitrary cosmological constant. We construct the most general solution of the GWs in the presence of a causal, timelike, or null boundary when the usual tensor modes are turned off. Our solution space besides the shape and topology of the wavefront which is a generic compact, smooth, and orientable $2d$ surface $Σ$, is specified by a vector…

This https://arxiv.org/abs/2401.15100 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Symmetry and classification of solutions to an integral equation in the Heisenberg group $\mathbb{H}^n$
In this paper we prove symmetry of nonnegative solutions of the integral equation \[ u (ζ) = \int\limits_{{\mathbb H}^n} |ζ^{-1} ξ|^{-(Q-α)} u(ξ)^{p} dξ\quad 1< p \leq \frac{Q+α}{Q-α},\quad 0< α

This https://arxiv.org/abs/2311.12782 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Quantum Imaging Beyond the Standard-Quantum Limit and Phase Distillation
Quantum sensing using non-linear interferometers offers the possibility of bicolour imaging, using light that never interacted with the object of interest, and provides a way to achieve phase supersensitivity, i.e. a Heisenberg-type scaling of the phase uncertainty. Such a scaling behaviour is extremely susceptible to noise and only arises at specific phases that define the optimal working point of the device. While phase-shifting algorithms are to some degree robust against the deleterious eff…

This https://arxiv.org/abs/2203.01307 has been replaced.
link: https://scholar.google.com/scholar?q=a

An $L^p$-spectral multiplier theorem with sharp $p$-specific regularity bound on Heisenberg type groups
We prove an $L^p$-spectral multiplier theorem for sub-Laplacians on Heisenberg type groups under the sharp regularity condition $s>d\left|1/p-1/2\right|$, where $d$ is the topological dimension of the underlying group. Our approach relies on restriction type estimates where the multiplier is additionally truncated along the spectrum of the Laplacian on the center of the group.

This https://arxiv.org/abs/2404.17207 has been replaced.
initial toot: https://mastoxiv.page/@arX…

Six magnetization plateau phases in a kagome antiferromagnet with $\rm{Y}_3\rm{Cu}_9(\rm{OH})_{19}\rm{Cl}_8$-type distortion
A recently discovered kagome antiferromagnet $\rm{Y}_3\rm{Cu}_9(\rm{OH})_{19}\rm{Cl}_8$ has attracted significant interest due to its unique kagome lattice structure and magnetic properties. Two separate studies have proposed distinct sets of exchange interaction parameters for this compound. In this study, we investigate the ground state of the spin-1/2 Heisenberg kagome model with three types of nearest-neighbor exchange interactions under a magnetic field by exact diagonalization using the L…

This https://arxiv.org/abs/2309.10957 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Approximation Algorithms for Quantum Max-$d$-Cut
We initiate the algorithmic study of the Quantum Max-$d$-Cut problem, a quantum generalization of the well-known Max-$d$-Cut problem. The Quantum Max-$d$-Cut problem involves finding a quantum state that maximizes the expected energy associated with the projector onto the antisymmetric subspace of two, $d$-dimensional qudits over all local interactions. Equivalently, this problem is physically motivated by the $SU(d)$-Heisenberg model, a spin glass model that generalized the well-known Heisenbe…

Phase diagram of the quantum spin-1/2 Heisenberg-$\Gamma$ model on a frustrated zigzag chain
Hidehiro Saito, Chisa Hotta
https://arxiv.org/abs/2404.10615 h…

Phase diagram of the quantum spin-1/2 Heisenberg-$Γ$ model on a frustrated zigzag chain
We investigate the quantum spin-1/2 zigzag chain with frustrated $J_1$-$J_2$ Heisenberg interactions, incorporating additional off-diagonal exchange interactions known as the $Γ$-term, both with and without an applied magnetic field. Based on the density-matrix renormalization group calculation, we map out the ground state phase diagram that shows a variety of magnetic and nonmagnetic phases including multicritical points and several exactly solvable points. Upon introducing a finite $Γ$-term…

Geometry of paraquaternionic contact structures
Marina Tchomakova, Stefan Ivanov, Simeon Zamkovoy
https://arxiv.org/abs/2404.16713 https://

Geometry of paraquaternionic contact structures
We introduce the notion of paraquaternionic contact structures (pqc structures), which turns out to be a generalization of the para 3-Sasakian geometry. We derive a distinguished linear connection preserving the pqc structure. Its torsion tensor is expressed explicitly in terms of the structure tensors. We define pqc-Einstein manifolds and show that para 3-Sasakian spaces are precisely pqc manifolds, which are pqc-Einstein. We introduce the paraquaternionic Heisenberg qroup and show that it is …

Phase diagram of the quantum spin-1/2 Heisenberg-$\Gamma$ model on a frustrated zigzag chain
Hidehiro Saito, Chisa Hotta
https://arxiv.org/abs/2404.10615 h…

Phase diagram of the quantum spin-1/2 Heisenberg-$Γ$ model on a frustrated zigzag chain
We investigate the quantum spin-1/2 zigzag chain with frustrated $J_1$-$J_2$ Heisenberg interactions, incorporating additional off-diagonal exchange interactions known as the $Γ$-term, both with and without an applied magnetic field. Based on the density-matrix renormalization group calculation, we map out the ground state phase diagram that shows a variety of magnetic and nonmagnetic phases including multicritical points and several exactly solvable points. Upon introducing a finite $Γ$-term…

This https://arxiv.org/abs/2311.12782 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Quantum Imaging Beyond the Standard-Quantum Limit and Phase Distillation
Quantum sensing using non-linear interferometers offers the possibility of bicolour imaging, using light that never interacted with the object of interest, and provides a way to achieve phase supersensitivity, i.e. a Heisenberg-type scaling of the phase uncertainty. Such a scaling behaviour is extremely susceptible to noise and only arises at specific phases that define the optimal working point of the device. While phase-shifting algorithms are to some degree robust against the deleterious eff…

Field-induced Peierls phase in $S=1$ Heisenberg spins coupled to quantum phonons
Shifeng Cui, Wenan Guo, G. G. Batrouni, Pinaki Sengupta
https://arxiv.org/abs/2404.06875

Field-induced Peierls phase in $S=1$ Heisenberg spins coupled to quantum phonons
Spin-Peierls transition occurs in a one-dimensional $S=1$ Heisenberg antiferromagnetic model with single-ion anisotropy, coupled to finite frequency bond phonons, in a magnetic field. Our results indicate that for the pure Heisenberg model, any Peierls transition is suppressed by quantum fluctuations of the phonon field. However, a novel magnetic field-induced Spin-Peierls phase is realized in the presence of strong single-ion anisotropy. Contrary to the standard Peierls state, the periodicity …

SU(3) altermagnetism: Lattice models, chiral magnons, and flavor-split bands
Pedro M. C\^onsoli, Matthias Vojta
https://arxiv.org/abs/2402.18629 https://…

SU(3) altermagnetism: Lattice models, chiral magnons, and flavor-split bands
Altermagnetism, a type of magnetic order that combines properties of ferromagnets and antiferromagnets, has generated significant interest recently, in particular due to its potential spintronics applications. Here, we show that altermagnetic states, which typically involve collinear magnetic order of SU(2) spins, can be generalized to higher SU($N$) symmetry groups. We construct a two-dimensional Heisenberg model for a three-sublattice SU(3) altermagnet and analyze its excitation spectrum via …

Decoherence-free algebras in quantum dynamics
Daniele Amato, Paolo Facchi, Arturo Konderak
https://arxiv.org/abs/2403.12926 https://a…

Decoherence-free algebras in quantum dynamics
In this Article we analyze the algebraic properties of the asymptotic dynamics of finite-dimensional open quantum systems in the Heisenberg picture. In particular, a natural product (Choi-Effros product) can be defined in the asymptotic regime. Motivated by this structure, we introduce a new space called the Choi-Effros decoherence-free algebra. Interestingly, this space is both a C* -algebra with respect to the composition product, and a B* -algebra with respect to the Choi-Effros product. Mor…

Comparing quantum fluctuations in the spin-$\frac{1}{2}$ and spin-$1$ XXZ Heisenberg models on square and honeycomb lattices
Masahiro Kadosawa, Masaaki Nakamura, Yukinori Ohta, Satoshi Nishimoto
https://arxiv.org/abs/2404.08099

Comparing quantum fluctuations in the spin-$\frac{1}{2}$ and spin-$1$ XXZ Heisenberg models on square and honeycomb lattices
We present a detailed investigation of the XXZ Heisenberg model for spin-$1/2$ and spin-$1$ systems on square and honeycomb lattices. Utilizing the density-matrix renormalization group (DMRG) method, complemented by Spiral Boundary Conditions (SBC) for mapping two-dimensional (2D) clusters onto one-dimensional (1D) chains, we meticulously explore the evolution of staggered magnetization and spin gaps across a broad spectrum of easy-axis anisotropies. Our study reveals that, despite the lower si…

This https://arxiv.org/abs/2310.08856 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Two-parameter estimation with single squeezed-light interferometer via double homodyne detection
The simultaneous two-parameter estimation problem in single squeezed-light Mach-Zehnder interferometer with double-port homodyne detection is investigated in this work. The analytical form of the two-parameter quantum Cramer-Bao bound defined by the quantum Fisher information matrix is presented, which shows the ultimate limit of the phase sensitivity will be further approved by the squeezed vacuum state. It can not only surpass the shot-noise limit, but also can even surpass the Heisenberg lim…

Six magnetization plateau phases in a kagome antiferromagnet with $\rm{Y}_3\rm{Cu}_9(\rm{OH})_{19}\rm{Cl}_8$-type distortion
Kazu Bodaiji, Katsuhiro Morita, Yoshiyuki Fukumoto
https://arxiv.org/abs/2404.17207

Six magnetization plateau phases in a kagome antiferromagnet with $\rm{Y}_3\rm{Cu}_9(\rm{OH})_{19}\rm{Cl}_8$-type distortion
A recently discovered kagome antiferromagnet $\rm{Y}_3\rm{Cu}_9(\rm{OH})_{19}\rm{Cl}_8$ has attracted significant interest due to its unique kagome lattice structure and magnetic properties. Two separate studies have proposed distinct sets of exchange interaction parameters for this compound. In this study, we investigate the ground state of the spin-1/2 Heisenberg kagome model with three types of nearest-neighbor exchange interactions under a magnetic field by exact diagonalization using the L…

Exchange Interactions in Rare-earth Magnets $A_2$PrO$_3$ ($A$= alkali metals): Revisited
Seong-Hoon Jang, Yukitoshi Motome
https://arxiv.org/abs/2404.17058

Exchange Interactions in Rare-earth Magnets $A_2$PrO$_3$ ($A$= alkali metals): Revisited
Rare-earth materials hold promise to realize exotic magnetic states owing to synergy between electron correlations and spin-orbit coupling. Recently, quasi-two-dimensional honeycomb magnets $A_2$PrO$_3$ ($A$ = alkali metals) were predicted to be good candidates for Kitaev quantum spin liquids, as the Kitaev-type bond-dependent anisotropic interactions dominate over bond-independent isotropic Heisenberg ones. However, experimental observations are negative, questioning the energy hierarchy in Pr…

This https://arxiv.org/abs/2312.01967 has been replaced.
initial toot: https://mastoxiv.page/@arX…

Kitaev-Heisenberg model on the star lattice -- from chiral Majoranas to chiral triplons
The interplay of frustrated interactions and lattice geometry can lead to a variety of exotic quantum phases. Here we unearth a particularly rich phase diagram of the Kitaev-Heisenberg model on the star lattice, a triangle decorated honeycomb lattice breaking sublattice symmetry. In the antiferromagnetic regime, the interplay of Heisenberg coupling and geometric frustration leads to the formation of valence bond solid (VBS) phases -- a singlet VBS and a bond selective triplet VBS stabilized by …

This https://arxiv.org/abs/2310.16080 has been replaced.
initial toot: https://mastoxiv.page/@arX…

Disorder effects in spiral spin liquids: Long-range spin textures, Friedel-like oscillations, and spiral spin glasses
Spiral spin liquids are correlated states of matter in which a frustrated magnetic system evades order by fluctuating between a set of (nearly) degenerate spin spirals. Here, we investigate the response of spiral spin liquids to quenched disorder in a $J_1$-$J_2$ honeycomb-lattice Heisenberg model. At the single-impurity level, we identify different order-by-quenched-disorder phenomena and analyze the ensuing spin textures. In particular, we show that the latter generally display Friedel-like o…

Quantum speed limit for Kirkwood-Dirac quasiprobabilities
Sagar Silva Pratapsi, Sebastian Deffner, Stefano Gherardini
https://arxiv.org/abs/2402.07582 http…

Quantum speed limit for Kirkwood-Dirac quasiprobabilities
What is the minimal time until a quantum system can exhibit genuine quantum features? To answer this question we derive quantum speed limits for two-time correlation functions arising from statistics of measurements. Generally, these two-time correlators are described by quasiprobabilities, if the initial quantum state of the system does not commute with the measurement observables. Our quantum speed limits are derived from the Heisenberg-Robertson uncertainty relation, and set the minimal time…

This https://arxiv.org/abs/2402.19079 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Experimental investigation of a multi-photon Heisenberg-limited interferometric scheme: the effect of imperfections
Interferometric phase estimation is an essential tool for precise measurements of quantities such as displacement, velocity and material properties. The lower bound on measurement uncertainty achievable with classical resources is set by the shot-noise limit (SNL) that scales asymptotically as $1/\sqrt{N}$, where $N$ is the number of resources used. The experiment of [S. Daryanoosh et al., Nat. Commun. ${\bf 9}$, 4606 (2018)] showed how to achieve the ultimate precision limit, the exact Heisenb…

This https://arxiv.org/abs/2310.07948 has been replaced.
initial toot: https://mastoxiv.page/@arX…

3D Heisenberg universality in the Van der Waals antiferromagnet NiPS$_3$
Van der Waals (vdW) magnetic materials are comprised of layers of atomically thin sheets, making them ideal platforms for studying magnetism at the two-dimensional (2D) limit. These materials are at the center of a host of novel types of experiments, however, there are notably few pathways to directly probe their magnetic structure. We report the magnetic order within a single crystal of NiPS$_3$ and show it can be accessed with resonant elastic X-ray diffraction along the edge of the vdW plane…