Tootfinder

Anomaly diagnosis via symmetry restriction in two-dimensional lattice systems
Kyle Kawagoe, Wilbur Shirley
https://arxiv.org/abs/2507.07430 https://…

Anomaly diagnosis via symmetry restriction in two-dimensional lattice systems
We describe a method for computing the anomaly of any finite unitary symmetry group $G$ acting by finite-depth quantum circuits on a two-dimensional lattice system. The anomaly is characterized by an index valued in the cohomology group $H^4(G,U(1))$, which generalizes the Else-Nayak index for locality preserving symmetries of quantum spin chains. We show that a nontrivial index precludes the existence of a trivially gapped symmetric Hamiltonian; it is also an obstruction to ``onsiteability" of…

On symmetry and exterior problems of knotted handlebodies
Yuya Koda, Makoto Ozawa, Yi-Sheng Wang
https://arxiv.org/abs/2506.06713 https://

On symmetry and exterior problems of knotted handlebodies
The paper concerns two classical problems in knot theory pertaining to knot symmetry and knot exteriors. In the context of a knotted handlebody $V$ in a $3$-sphere $S^3$, the symmetry problem seeks to classify the mapping class group of the pair $(S^3,V)$, whereas the exterior problem examines to what extent the exterior $E(V)$ determines or fails to determine the isotopy type of $V$. The paper determines the symmetries of knotted genus two handlebodies arising from hyperbolic knots with non-in…

Unified constructions of the regular Heptagon and Triskaidecagon
Helmut Ruhland
https://arxiv.org/abs/2505.05673 https://arxiv.org/pd…

Unified constructions of the regular Heptagon and Triskaidecagon
Constructions of regular heptagon and triskaidecagon by trisection of an angle are well known. An elegant construction of the heptagon by S. Adlaj shows a 3-fold symmetry related to a Galois group. Based on the later construction, in this article one more for the heptagon and two more for the triskaidecagon are presented, all using angle trisection.

This https://arxiv.org/abs/2506.01272 has been replaced.
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Hadrons in group expansion
Various approximate symmetries exist in nature. For example, the flavor $SU(4)$ symmetry involving the $up/down/strange/charm$ quarks is severely broken, the flavor $SU(3)$ symmetry involving the $up/down/strange$ quarks is moderately broken, and the isospin $SU(2)$ symmetry involving the $up/down$ quarks is slightly broken. These broken symmetries are primarily governed by the strong interaction, making them an ideal platform for investigating the general behavior of approximate symmetries. To…

Orbifold Saito theory of A and D type singularities
Alexey Basalaev, Anton Rarovskii
https://arxiv.org/abs/2507.07609 https://arxiv.o…

Orbifold Saito theory of A and D type singularities
Saito theory associates to an isolated singularity rich structure that plays an important role in mirror symmetry. In this note we construct Saito theory for A and D type Landau--Ginzburg orbifolds. Namely, for the pairs $(f,G)$, where $f$ defines an isolated singularity of A and D type and $G$ is a group of symmetries of $f$. In total we consider five families of such pairs. In particular, we construct the orbifold versions of Brieskorn lattice and the Gauss--Manin connection computing them ex…

Mutual Influence of Symmetries and Topological Field Theories
Daniel Teixeira, Matthew Yu
https://arxiv.org/abs/2507.06304 https://ar…

Mutual Influence of Symmetries and Topological Field Theories
We study how the fusion 2-category symmetry of a fermionic (2+1)d QFT can be affected when one allows for stacking with TQFTs to be an equivalence relation for QFTs. Focusing on a simple kind of fermionic fusion 2-category described purely by group theoretical data, our results reveal that by allowing for stacking with $\mathrm{Spin}(n)_1$ as an equivalence relation enables a finite set of inequivalent modifications to the original fusion 2-categorical-symmetry. To put our results in a broader …

Dynamical group approach to conformal field theory
G. A. Kerimov
https://arxiv.org/abs/2507.02786 https://arxiv.org/pdf/2507.02786

Dynamical group approach to conformal field theory
We propose a purely group-theoretical method for describing the S-matrix in quantum field theory with dynamical symmetry. In this approach, the Heisenberg S-matrix in a QFT with dynamical symmetry is an intertwining operator between unitary representations of the underlining dynamical group acting in Hilbert spaces spanned by the 'in' and 'out' states. As application we consider scalar Euclidean QFT with conformal symmetry.

Symmetry Classification for Alternating Excitons in Two-Dimensional Altermagnets
Jiayu David Cao, Konstantin S. Denisov, Yuntian Liu, Igor Zutic
https://arxiv.org/abs/2506.05753

Symmetry Classification for Alternating Excitons in Two-Dimensional Altermagnets
Excitons, bound electron-holes states, often dominate the optical response of two-dimensional (2D) materials and reflect their inherent properties, including spin-orbit coupling, magnetic ordering, or band topology. By focusing on a growing class of collinear antiferromagnets with a nonrelativistic spin splitting, referred to also as altermagnets (AM), we propose a theoretical framework based on the spin space group (SSG) to elucidate their resulting excitons. Our approach is illustrated on 2D …

This https://arxiv.org/abs/2411.01824 has been replaced.
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Imprinting electrically switchable scalar spin chirality by anisotropic strain in a Kagome antiferromagnet
Topological chiral antiferromagnets, such as Mn$_{3}$Sn, are emerging as promising materials for next-generation spintronic devices due to their intrinsic transport properties linked to exotic magnetic configurations. Here, we demonstrate that anisotropic strain in Mn$_{3}$Sn thin films offers a novel approach to manipulate the magnetic ground state, unlocking new functionalities in this material. Anisotropic strain reduces the point group symmetry of the manganese (Mn) Kagome triangles from $C…

From Signed Networks to Group Graphs
Tim S. Evans
https://arxiv.org/abs/2505.22802 https://arxiv.org/pdf/2505.22802

From Signed Networks to Group Graphs
I show that when there is a symmetry in a process defined on the nodes of a network, this can be captured by a new structure, the ``group graph'', in which group elements label the links of a network. I show that group graphs are a generalisation of signed networks which are an example of a $Z_2$ group graph. I also show that the concept of balance in signed networks can be generalised to group graphs. Finally, I show how the dynamics of processes on a consistent group graph are completely cont…

Gravitational Wave Signals in a Promising Realization of SO(10) Unification
Injun Jeong (Center for Quantum Spacetime, Sogang University, Department of Physics, Sogang University), J\"orn Kersten (Department of Physics and Technology, University of Bergen, Department of Physics and IPAP, Yonsei University), Stefano Scopel (Center for Quantum Spacetime, Sogang University, Department of Physics, Sogang University), Liliana Velasco-Sevilla (Center for Quantum Spacetime, Sogang Univer…

Gravitational Wave Signals in a Promising Realization of SO(10) Unification
We investigate gravitational wave signals in a non-supersymmetric grand unified model where the group $SO(10)$ is broken in two steps to the Standard Model gauge group. We calculate the analytical form of the one-loop effective potential responsible for the first step of symmetry breaking and show that it can lead to a first-order phase transition with gravitational wave production. We also determine the gravitational wave background produced by the primordial plasma of relativistic particles. …

Why there is no Love in black holes
Alexandru Lupsasca
https://arxiv.org/abs/2506.05298 https://arxiv.org/pdf/2506.05298

Why there is no Love in black holes
This paper presents a new conformal symmetry of stationary, axisymmetric Kerr perturbations. This symmetry is exact but non-geometric (or "hidden"), and each of its generators has an associated infinite family of eigenstate solutions. Tidal perturbations of a black hole form an irreducible highest-weight representation of this conformal group, while the tidal response fields live in a different such representation. This implies that black holes have no tidal deformability, or vanishing Love num…

Partial Group Symmetry in Figures I: Semidirect Products and the Six Coins
Takahiro Hayashi
https://arxiv.org/abs/2506.14304 https://…

Partial Group Symmetry in Figures I: Semidirect Products and the Six Coins
In this paper, we construct a partial group \(\mathcal{P}(F)\) that represents the "partial symmetry" inherent in a subset \(F\) of \(d\)-dimensional Euclidean space. In cases where \(F\) is not connected, \(\mathcal{P}(F)\) captures more detailed information than the conventional symmetry group \(G(F)\). To establish a stronger connection between \(\mathcal{P}(F)\) and \(F\), we introduce a novel definition of partial group action. Furthermore, to characterize \(\mathcal{P}(F)\) in specific ca…

This https://arxiv.org/abs/2407.08438 has been replaced.
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Symmetries of power-free integers in number fields and their shift spaces
We describe the group of $\mathbb Z$-linear automorphisms of the ring of integers of a number field $K$ that preserve the set $V_{K,k}$ of $k$th power-free integers: every such map is the composition of a field automorphism and the multiplication by a unit. We show that those maps together with translations generate the extended symmetry group of the shift space $\mathbb D_{K,k}$ associated to $V_{K,k}$. Moreover, we show that no two such dynamical systems $\mathbb D_{K,k}$ and $\mathbb D_{L,…

This https://arxiv.org/abs/2309.03765 has been replaced.
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Equivariant Symmetries for Inertial Navigation Systems
This paper investigates the problem of inertial navigation system (INS) filter design through the lens of symmetry. The extended Kalman filter (EKF) and its variants have been the staple of INS filtering for 50 years. However, recent advances in inertial navigation systems have exploited matrix Lie group structure to design stochastic filters and state observers that have been shown to display superior performance compared to classical solutions. In this work, we explore various symmetries of i…

Little $q$-Jacobi polynomials and symmetry breaking operators for $U_q(sl_2)$
Quentin Labriet, Lo\"ic Poulain d'Andecy
https://arxiv.org/abs/2506.23848

Little $q$-Jacobi polynomials and symmetry breaking operators for $U_q(sl_2)$
This paper presents explicit formulas for intertwining operators of the quantum group $U_q(sl_2)$ acting on tensor products of Verma modules. We express a first set of intertwining operators (the holographic operators) in terms of the little $q$-Jacobi polynomials, and we obtain for the dual set (the symmetry breaking operators) a $q$-deformation of the Rankin--Cohen operators. The Verma modules are realised on polynomial spaces and, interestingly, we find along the way the need to work with no…

Poset-Markov Channels: Capacity via Group Symmetry
Eray Unsal Atay, Eitan Levin, Venkat Chandrasekaran, Victoria Kostina
https://arxiv.org/abs/2506.19305 h…

Poset-Markov Channels: Capacity via Group Symmetry
Computing channel capacity is in general intractable because it is given by the limit of a sequence of optimization problems whose dimensionality grows to infinity. As a result, constant-sized characterizations of feedback or non-feedback capacity are known for only a few classes of channels with memory. This paper introduces poset-causal channels$\unicode{x2014}$a new formalism of a communication channel in which channel inputs and outputs are indexed by the elements of a partially ordered set…

Partial Compositeness: from Anarchy to Symmetry
Kaustubh Agashe, Lorenzo Ricci, Raman Sundrum
https://arxiv.org/abs/2507.05332 https://

Partial Compositeness: from Anarchy to Symmetry
Within the Composite Higgs paradigm, Partial Compositeness has emerged as an elegant mechanism for generating large flavor hierarchies such as are observed in the quark and lepton masses and mixings. This mechanism exploits the strong renormalization group effects of the compositeness dynamics when these are {\it not} flavor-symmetric. Despite its remarkable properties, at this point it is stringently constrained by the body of flavor- and CP-violation tests, so that the compositeness scale mus…

One dimensional Bose-Hubbard model with long range hopping
Edmond Orignac
https://arxiv.org/abs/2506.03629 https://arxiv.org/pdf/2506…

One dimensional Bose-Hubbard model with long range hopping
Interacting one-dimensional bosons with long range hopping decaying as a power law $r^{-α}$ with distance $r$ are considered with the renormalization group and the self-consistent harmonic approximation. For $α\ge 3$, the ground state is always a Tomonaga-Luttinger liquid, whereas for $α<3$, a ground state with long range order breaking the continuous global gauge symmetry becomes possible for sufficiently weak repulsion. At positive temperature, continuous symmetry breaking becomes restrict…

This https://arxiv.org/abs/2505.19452 has been replaced.
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Nonsymmorphic symmetry adapted finite element modeling of glide-symmetric photonic structures
Space group theory is pivotal in the design of nanophotonics devices, enabling the characterization of periodic optical structures such as photonic crystals. The aim of this study is to extend the application of nonsymmorphic space groups in the field of numerical analysis for research and design of nanophotonics devices. In this work, we introduce the nonsymmorphic symmetry adapted finite element method, and provide a systematic approach for efficient band structure analysis of photonic struct…

Dynamical decoupling of interacting spins through group factorization
Colin Read, Eduardo Serrano-Ens\'astiga, John Martin
https://arxiv.org/abs/2506.15382

Dynamical decoupling of interacting spins through group factorization
Dynamical decoupling (DD) is a well-known open-loop protocol for suppressing unwanted interactions in a quantum system, thereby drastically extending the coherence time of useful quantum states. In the original framework of evolution symmetrization, a DD sequence was shown to enforce a symmetry on the unwanted Hamiltonian, thereby suppressing it if the symmetry was inaccessible. In this work, we show how symmetries already present in the undesired Hamiltonian can be harnessed to reduce the comp…

This https://arxiv.org/abs/2408.00067 has been replaced.
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Monopole Breaking of Chern-Weil Symmetries
Gauge theories in $d$ dimensions with a nontrivial fundamental group admit a $(d-3)$-form magnetic symmetry and a $(d-5)$-form instantonic symmetry. These are examples of Chern-Weil symmetries, with conserved currents built out of the gauge field strength, which can only be explicitly broken through violations of the Bianchi identity. For U(1) gauge theory, it is clear that magnetic monopoles violate not only the $(d-3)$-form magnetic symmetry but also lower-form symmetries like the instantonic…

Topologically Distinct Berry Phases in a Single Triangular M\"obius Microwave Resonator
E. C. I. Paterson, M. E. Tobar, M. Goryachev, J. Bourhill
https://arxiv.org/abs/2506.07320

Topologically Distinct Berry Phases in a Single Triangular Möbius Microwave Resonator
We report the experimental observation of two distinct Berry phases ($+\frac{2π}{3}$ and $-\frac{2π}{3}$) generated on the surface of a Möbius cavity resonator at microwave frequencies supporting the TE$_{1,0,n}$ mode family. This resonator consists of a twisted, mirror-asymmetric prism with a cross-section of the triangular $D_3$ symmetry group, bent around on itself to form a ring. This geometric class supports resonant modes with non-zero electromagnetic helicity (i.e. nonzero $\vec{E}\cd…

This https://arxiv.org/abs/2412.13320 has been replaced.
initial toot: https://mastoxiv.page/@arX…

Density Matrix Renormalization Group simulations of the SU(N) Fermi-Hubbard chain implementing the full SU(N) symmetry via Semi-Standard Young Tableaux and Unitary Group Subduction Coefficients
We have developed an efficient method for performing density matrix renormalization group (DMRG) simulations of the SU(N) Fermi-Hubbard chain with open boundary conditions, fully leveraging the SU(N) symmetry of the problem. This method extends a previously developed approach for the SU(N) Heisenberg model and relies on the systematic use of the semi-standard Young tableaux (SSYT) basis in a DMRG algorithm `a la White. Specifically, the method aligns the site-by-site growth process of the infin…

A remarkable dynamical symmetry of the Landau problem
Tekin Dereli, Philippe Nounahon, Todor Popov
https://arxiv.org/abs/2506.11642 https://

A remarkable dynamical symmetry of the Landau problem
We show that the dynamical group of an electron in a constant magnetic field is the group of symplectomorphisms $Sp(4,\mathbb{R})$. It is generated by the spinorial realization of the conformal algebra $\mathfrak{so}(2,3)$ considered in Dirac's seminal paper "A Remarkable Representation of the 3 + 2 de Sitter Group". The symplectic group $Sp(4,\mathbb{R})$ is the double covering of the conformal group $SO(2,3)$ of 2+1 dimensional Minkowski spacetime which is in turn the dynamical group of a hyd…

Charge quantisation, monopoles and emergent symmetry in the Standard Model and its embeddings
Rodrigo Alonso, Despoina Dimakou, Yunji Ha, Valentin V. Khoze
https://arxiv.org/abs/2507.01777

Charge quantisation, monopoles and emergent symmetry in the Standard Model and its embeddings
This work studies the connection of the global properties of the SM gauge group to 1-form discrete symmetries, the possible non-Abelian embeddings of the SM group, and electric and magnetic charge quantisation. Building on previous work, we introduce indexes to characterise the group choices, connect the concept of compositeness degree to emergent electric 1-form symmetry, introduce a new model to fill in the $p=1$ gap, and analyse the magnetic spectrum while connecting its UV and IR realisatio…

Ginzburg-Landau theory for unconventional surface superconductivity in PtBi$_2$
Harald Waje, Fabian Jakubczyk, Jeroen van den Brink, Carsten Timm
https://arxiv.org/abs/2507.02415 …

Ginzburg-Landau theory for unconventional surface superconductivity in PtBi$_2$
Recent experimental evidence suggests the presence of an unconventional, nodal surface-superconducting state in trigonal PtBi\textsubscript{2}. We construct a Ginzburg--Landau theory for the three superconducting order parameters, which correspond to the three irreducible representations of the point group $C_{3v}$. The irreducible representations $A_1$ and $A_2$ are the most likely. We develop a systematic method to determine the symmetry-allowed terms and apply it to derive all terms up to fo…

Symmetry groups of origami structures
Sara Chari, Andrew Quinn Macauley
https://arxiv.org/abs/2506.19177 https://arxiv.org/pdf/2506.1…

Symmetry groups of origami structures
Origami is the art of folding paper into various patterns without cutting or tearing the paper. By viewing the paper as the complex plane, we iteratively compute and record all intersection points to construct mathematical origami sets. Additionally, we include the various lines to create a repeating pattern that can be viewed as a wallpaper group if the angle set contains fewer than 3 angles. There are 17 wallpaper groups up to isomorphism, so we determine which such groups can be constructed …

$\mathrm{SL}(2,\mathbb{R})$ families of Kerr black holes
Robert Penna
https://arxiv.org/abs/2506.00184 https://arxiv.org/pdf/2506.001…

$\mathrm{SL}(2,\mathbb{R})$ families of Kerr black holes
The stationary, axisymmetric sector of vacuum general relativity (with zero cosmological constant) enjoys an $\mathrm{SL}(2,\mathbb{R})$ symmetry called the Matzner-Misner group. We study the action of the Matzner-Misner group on the Kerr black hole. We show that the group acts naturally on a three parameter generalization of the usual two parameter Kerr solution. The new parameter represents a large diffeomorphism which gives the spacetime an asymptotic angular velocity. We explain how the $\m…

Iterated finite group actions on closed connected aspherical manifolds
Jordi Daura Serrano
https://arxiv.org/abs/2506.13184 https://a…

Iterated finite group actions on closed connected aspherical manifolds
In this paper we use free iterated actions and the iterated discrete degree of symmetry to obtain rigidity results on aspherical manifolds. We also introduce the concept of the length of an iterated action and we study it for nilmanifolds, solvmanifolds and locally symmetric spaces.

This https://arxiv.org/abs/2412.11569 has been replaced.
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The dark side of the forces: assessing non-conservative force models for atomistic machine learning
The use of machine learning to estimate the energy of a group of atoms, and the forces that drive them to more stable configurations, has revolutionized the fields of computational chemistry and materials discovery. In this domain, rigorous enforcement of symmetry and conservation laws has traditionally been considered essential. For this reason, interatomic forces are usually computed as the derivatives of the potential energy, ensuring energy conservation. Several recent works have questioned…

$\displaystyle SL(2, {\Bbb Z})$, les tresses \`a trois brins, le tore modulaire et $Aut^{ }(F_{2})$
Alexis Marin
https://arxiv.org/abs/2506.19371 https://

$\displaystyle SL(2, {\Bbb Z})$, les tresses à trois brins, le tore modulaire et $Aut^{+}(F_{2})$
The action of $SL(2, {\bf Z})$ on the integer torus and its quotient by central symmetry and Artin's presentation of three strings braid group $B_{3}$, produces a presentation with parabolic generators $\pmatrix{1& -1\cr 0& 1\cr}$ and $\pmatrix{1& 0\cr 1& 1\cr}$. This braided presentation describes the action of the derived group on Poincaré's half plane and its quotient the modular torus, just as Nielsen's theorem giving the group of direct automorphisms of the free group on two generators as…

Hadrons in group expansion
Hua-Xing Chen
https://arxiv.org/abs/2506.01272 https://arxiv.org/pdf/2506.01272

Hadrons in group expansion
Various approximate symmetries exist in nature. For example, the flavor $SU(4)$ symmetry involving the $up/down/strange/charm$ quarks is severely broken, the flavor $SU(3)$ symmetry involving the $up/down/strange$ quarks is moderately broken, and the isospin $SU(2)$ symmetry involving the $up/down$ quarks is slightly broken. These broken symmetries are primarily governed by the strong interaction, making them an ideal platform for investigating the general behavior of approximate symmetries. To…

Instability of the Haldane Phase: Roles of Charge Fluctuations and Hund's Coupling
Satoshi Nishimoto
https://arxiv.org/abs/2507.05089 https://

Instability of the Haldane Phase: Roles of Charge Fluctuations and Hund's Coupling
We systematically investigate the stability of the symmetry-protected topological (SPT) Haldane phase in spin-1/2 Heisenberg and half-filled Hubbard ladders coupled by ferromagnetic Hund's interactions. Using density-matrix renormalization group (DMRG) method, we analyze key signatures of the Haldane phase: long-range string order, finite spin gap, and characteristic entanglement spectrum degeneracies. In spin-only Heisenberg ladders, we find immediate onset and continuous strengthening of the …

Large and iterated finite group actions on manifolds admitting non-zero degree maps to nilmanifolds
Jordi Daura Serrano
https://arxiv.org/abs/2506.11174 ht…

Large and iterated finite group actions on manifolds admitting non-zero degree maps to nilmanifolds
Let M be a closed connected oriented manifold admitting a non-zero degree map to a nilmanifold. In the first part of the paper we study effective finite group actions on M. In particular, we prove that Homeo(M) is Jordan, we bound the discrete degree of symmetry of M and we study the number and the size of stabilizers of an effective action of a finite group G on M. We also study the toral rank conjecture and Carlsson's conjecture for large primes for this class of manifolds. In the second part…

Homomorphism, substructure and ideal: Elementary but rigorous aspects of renormalization group or hierarchical structure of topological orders
Yoshiki Fukusumi, Yuma Furuta
https://arxiv.org/abs/2506.23155

Homomorphism, substructure and ideal: Elementary but rigorous aspects of renormalization group or hierarchical structure of topological orders
We study ring homomorphisms between fusion rings appearing in conformal field theories connected under massless renormalization group (RG) flows. By interpreting the elementary relationship between homomorphism, quotient ring, and projection, we propose a general quantum Hamiltonian formalism of a massless and massive RG flow with an emphasis on generalized symmetry. In our formalism, the noninvertible nature of the ideal of a fusion ring plays a fundamental role as a condensation rule between …

Sampling Finite Unit Norm Tight Frames Using Symplectic Geometry
Mason Faldet, Clayton Shonkwiler
https://arxiv.org/abs/2505.22847 https://

Sampling Finite Unit Norm Tight Frames Using Symplectic Geometry
Unit-norm tight frames in finite-dimensional Hilbert spaces (FUNTFs) are fundamental in signal processing, offering optimal robustness to noise and measurement loss. In this paper we introduce the Eigenlift algorithm for sampling random FUNTFs. Our approach exploits the symplectic geometry of the FUNTF space, which we characterize as a symplectic reduction of frame space by a symmetry group. We then define a Hamiltonian torus action on this reduced space whose momentum map induces a fiber bundl…

Optically Addressing Circularly-Polarized Vibrations in Molecules
Chientzu Lin, Connor K. Terry Weatherly, Roel Tempelaar
https://arxiv.org/abs/2506.20827 …

Optically Addressing Circularly-Polarized Vibrations in Molecules
Circularly-polarized (CP) vibrations are the nuclear-motion analog of CP light, emerging in molecules with non-Abelian point-group symmetry that support orthogonal and degenerate vibrational normal modes. Here, we explore the optical addressability of CP vibrations, motivated by their potential as nanoscale angular momentum states suitable for information storage and manipulation. We investigate how symmetry-breaking chemical modifications affect a molecule's capacity to support CP vibrations. …

Triplet nodal lines and Chern bands in XCuCl$_{3}$ (X= K, Tl)
Charles B. Walker, Matthew Stern, Judit Romh\'anyi
https://arxiv.org/abs/2507.00285 https…

Triplet nodal lines and Chern bands in XCuCl$_{3}$ (X= K, Tl)
We investigate the symmetry-enforced line nodes of the triplet excitations of XCuCl$_{3}$ (X= K, Tl), showing that they are protected by the nonsymmorphic symmetries and are unaffected by the microscopic details, such as interaction and anisotropy strength, as long as the ground state and the symmetry group remain unaltered. Extending the conventionally used isotropic spin model for XCuCl$_{3}$, our analysis includes all the symmetry-allowed anisotropies and gives a detailed account of the role…

Compound Burgers-KdV Soliton Behaviour: Refraction, Reflection and Fusion
Darryl D. Holm, Ruiao Hu, Oliver D. Street, Hanchun Wang
https://arxiv.org/abs/2505.17026

Compound Burgers-KdV Soliton Behaviour: Refraction, Reflection and Fusion
We consider a coupled PDE system between the Burgers equation and the KdV equation to model the interactions between `bore'-like structures and wave-like solitons in shallow water. Two derivations of the resulting Burgers-swept KdV system are presented, based on Lie group symmetry and reduced variational principles. Exact compound soliton solutions are obtained, and numerical simulations show that the Burgers and KdV momenta tend toward a balance at which the coupled system reduces to the integ…

Functional renormalization group study of anomalous magnetic moment in a low energy effective theory
Rui Wen, Chuang Huang, Mei Huang
https://arxiv.org/abs/2506.20246

Functional renormalization group study of anomalous magnetic moment in a low energy effective theory
The quark anomalous magnetic moments (AMMs) are investigated in a 2-flavor low-energy effective theory within the functional renormalization group (FRG) approach under an external magnetic field. The Schwinger formalism is adopted for quark propagators, and Fierz-complete four-quark scatterings are self-consistently included through the renormalization group flows. We find that the quark AMMs are dynamically generated with the chiral symmetry breaking, and the magnitude of the AMM of the down q…

Quantum multicriticality and emergent symmetry in Dirac systems with two order parameters at three-loop order
Max Uetrecht, Igor F. Herbut, Michael M. Scherer, Emmanuel Stamou, Tom Steudtner
https://arxiv.org/abs/2505.22723

Quantum multicriticality and emergent symmetry in Dirac systems with two order parameters at three-loop order
Two-dimensional materials with interacting Dirac excitations can host quantum multicritical behavior near the phase boundaries of the semimetallic and two-ordered phases. We study such behavior in Gross--Neveu--Yukawa field theories where $N_f$ flavors of Dirac fermions are coupled to two order-parameter fields with $SO(N_A)$ and $SO(N_B)$ symmetry, respectively. To that end, we employ the perturbative renormalization group up to three-loop order in $4-ε$ spacetime dimensions. We distinguish t…

Dark matter mixing within the seesaw type II mechanism in the left-right symmetric model
M. Dubinin, E. Fedotova, D. Kazarkin
https://arxiv.org/abs/2506.04035

Dark matter mixing within the seesaw type II mechanism in the left-right symmetric model
The seesaw type II mechanism is considered within the framework of a left-right chiral model with a gauge group $SU(2)_L\times SU(2)_R\times U(1)$, the lepton sector of which includes three generations of heavy Majorana neutrinos. The dependence of the mixing parameters of the lightest sterile neutrino as a dark matter particle on the scales of left-right symmetry breaking in the case of direct and inverse hierarchies of active neutrino masses is analyzed.

Two-neutrino $0^ \to 0^ $ double beta decay of $^{48}\mathrm{Ca}$ within the DFT-NCCI framework
Jan Mi\'skiewicz, Maciej Konieczka, Wojciech Satu{\l}a
https://arxiv.org/abs/2506.13747

Two-neutrino $0^+ \to 0^+$ double beta decay of $^{48}\mathrm{Ca}$ within the DFT-NCCI framework
We present a seminal calculation of the nuclear matrix element for the two-neutrino double beta ($2νββ$) decay of ${}^{48}\text{Ca} \rightarrow {}^{48}\text{Ti}$ using a post-Hartree-Fock (HF) Density Functional Theory-based No-Core Configuration-Interaction (DFT-NCCI) framework developed by our group [Phys. Rev. C 94, 024306 (2016)]. In the present calculation, we utilize a variant of the approach that restores rotational symmetry and mixes states projected from self-consistent mean-field c…

Kondo-Peierls transition with nonsymmorphic zone boundary gap formation
Kazumasa Hattori, Hiroaki Kusunose
https://arxiv.org/abs/2506.21313 https://…

Kondo-Peierls transition with nonsymmorphic zone boundary gap formation
We study nonsymmorphic space group symmetry breakings in correlated electron systems. Under nonsymmorphic symmetry, it is well known that there are degeneracies in the electronic Bloch states at the Brillouin zone boundaries. When the system undergoes a phase transition into an ordered phase with breaking the nonsymmorphic symmetry, the degeneracy is lifted. This happens even when the order parameter is uniform. We point out that this general feature leads to various {\it uniform} Peierls trans…

Symmetries of weighted networks: weight approximation method and its application to food webs
Julia Korol, Mateusz Iskrzy\'nski
https://arxiv.org/abs/2506.11824

Symmetries of weighted networks: weight approximation method and its application to food webs
Knowing which parts of a complex system have identical roles simplifies computations and reveals patterns in its network structure. Group theory has been applied to study symmetries in unweighted networks. However, in real-world weighted networks, edge weights are rarely equal, making exact symmetry uncommon. To study symmetries in weighted networks, we aggregate edge weights into a small number of discrete categories. The symmetries of these aggregated networks identify vertices with similar r…

Non-holomorphic modular flavor symmetry and odd weight polyharmonic Maa{\ss} form
Bu-Yao Qu, Jun-Nan Lu, Gui-Jun Ding
https://arxiv.org/abs/2506.19822 http…

Non-holomorphic modular flavor symmetry and odd weight polyharmonic Maaß form
We extend the framework of non-holomorphic modular flavor symmetry to include the odd weight polyharmonic Maaß forms. The integer weight polyharmonic Maaß forms of level $N$ can be arranged into multipltets of the homogeneous finite modular group $Γ'_N$. We propose to construct the integer weight, including weight one, non-holomorphic polyharmonic Maaß forms from the non-holomorphic Eisenstein series. The previous results of even weight polyharmonic Maaß forms are reproduced. We apply this…

The building blocks of asymptotically flat spacetimes
Shadi Ali Ahmad
https://arxiv.org/abs/2506.11190 https://arxiv.org/pdf/2506.111…

The building blocks of asymptotically flat spacetimes
The classification of all possible induced representations arising from theories admitting a Poincaré symmetry has molded our very conception of particles in flat space. In this note, we argue that if one takes the same viewpoint on the asymptotic symmetry group instead of the global one, the familiar relativistic classification is enhanced to provide a new notion of excitations in asymptotically flat spacetimes. These excitations blur the line between the quantum description of a particle and…

This https://arxiv.org/abs/2504.07180 has been replaced.
initial toot: https://mastoxiv.page/@arX…

Fixed Point Stability Switches from Attractive to Repulsive at 2d Pomeranchuk/Stoner Instabilities via Field-Theoretical RG
We study an interacting two-flavor fermionic system via field-theoretical functional renormalization group (RG). Each flavor, labeled by $\pm$, has a dispersion of $E^{\pm}=c k^{2α}-μ^\pm$ with tunable real exponent $α>0$. The effective theory is parametrized by intra-flavor and inter-flavor interactions, preserving global U(1) $\times$ U(1) symmetry, which can be enhanced to U(2). The U(2) symmetric system has a Fermi liquid phase and two possible instabilities, leading to spontaneous spati…

Enhancement of axial anomaly effects in hot two-color QCD: FRG approach in the linear sigma model
Gergely Fej\H{o}s, Daiki Suenaga
https://arxiv.org/abs/2506.14010

Enhancement of axial anomaly effects in hot two-color QCD: FRG approach in the linear sigma model
We investigate the thermal properties of hadrons in two-color quantum chromodynamics (QC$_2$D) using the functional renormalization group (FRG) method, with particular focus on modifications of the $U(1)$ axial anomaly effects. The hadrons are described by a linear sigma model (LSM) based on the Pauli-Gürsey $SU(4)$ symmetry, which incorporates both low-lying $0^\pm$ mesons and diquark baryons. We find that all quartic couplings are comparably suppressed when physical values of the pion mass a…