Tootfinder

This https://arxiv.org/abs/2401.16619 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Quantum algorithms for calculating determinant and inverse of matrix and solving linear algebraic systems
We propose quantum algorithms, purely quantum in nature, for calculating the determinant and inverse of an $(N-1)\times (N-1)$ matrix (depth is $O(N^2\log N)$) which is a simple modification of the algorithm for calculating the determinant of an $N\times N$ matrix (depth is $O(N\log^2 N)$. The basic idea is to encode each row of the matrix into a pure state of some quantum system. In addition, we use the representation of the elements of the inverse matrix in terms of algebraic complements. Thi…

Roughening and dynamics of an electric flux string in a (2 1)D lattice gauge theory
Francesco Di Marcantonio, Sunny Pradhan, Sofia Vallecorsa, Mari Carmen Ba\~nuls, Enrique Rico Ortega
https://arxiv.org/abs/2505.23853

Roughening and dynamics of an electric flux string in a (2+1)D lattice gauge theory
We investigate the roughening transition in the pure $\mathbb{Z}_2$ lattice gauge theory in (2+1) dimensions. Using numerical simulations with matrix product states, we explore the static and dynamical properties of an electric flux string between two static charges as the coupling is varied and approaches the deconfinement phase transition from the confined phase. Within the roughening region, we obtain the universal Lüscher correction to the confining potential and observe the expected resto…

Eigenstate Thermalization Hypothesis (ETH) for off-diagonal matrix elements in integrable spin chains
Federico Rottoli, Vincenzo Alba
https://arxiv.org/abs/2505.23602

Eigenstate Thermalization Hypothesis (ETH) for off-diagonal matrix elements in integrable spin chains
We investigate off-diagonal matrix elements of local operators in integrable spin chains, focusing on the isotropic spin-$1/2$ Heisenberg chain ($XXX$ chain). We employ state-of-the-art Algebraic Bethe Ansatz results, which allow us to efficiently compute matrix elements of operators with support up to two sites between generic energy eigenstates. We consider both matrix elements between eigenstates that are in the same thermodynamic macrostate, as well as eigenstates that belong to different m…

Emergent Quasiparticles \& Field-Tuned RIXS Spectra in a Trimerized Spin-1/2 Chain
Subhajyoti Pal, Pradeep Thakur, Ashis Kumar Nandy, Anamitra Mukherjee
https://arxiv.org/abs/2505.23208

Emergent Quasiparticles \& Field-Tuned RIXS Spectra in a Trimerized Spin-1/2 Chain
We investigate spin-flip excitations in the spin-1/2 trimer chain $\rm{Cu_3(P_2O_6OH)_2}$, featuring an antiferromagnetic exchange motif $J_1$-$J_1$-$J_2$ with $J_1 < J_2$. Using density matrix renormalization group (DMRG) simulations, we demonstrate that single-spin-flip processes induced by resonant inelastic X-ray scattering (RIXS) generate emergent gapless modes governed by the underlying trimer periodicity alongside distinct high-energy excitations. By combining exact diagonalization and r…

This https://arxiv.org/abs/2505.03551 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

From Mass-Shell Factorisation to Spin: An Attempt at a Matrix-Valued Liouville Framework for Relativistic Classical and Quantum Phase-Spacetime
While Liouville's theorem is first-order in time for the phase-space distribution itself, the relativistic mass-shell constraint $p^μp_μ= m^2$ is naively second-order in energy. We argue that it is reasonable to unify both energy branches within a single Hamiltonian by factorizing $(p^2 - m^2)$ in analogy with Dirac's approach in relativistic quantum mechanics. We show the resulting matrix-based Liouville equation remains first order and naturally yields a $4\times4$ matrix-valued probability…

This https://arxiv.org/abs/2412.20140 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Self-similarity on 4d cubic lattice
A phenomenon of "algebraic self-similarity" on 3d cubic lattice, providing what can be called an algebraic analogue of Kadanoff--Wilson theory, is shown to possess a 4d version as well. Namely, if there is a $4\times 4$ matrix $A$ whose entries are indeterminates over the field $\mathbb F_2$, then the $2\times 2\times 2\times 2$ block made of sixteen copies of $A$ reveals the existence of four direct "block spin" summands corresponding to the same matrix $A$. Moreover, these summands can be wri…

This https://arxiv.org/abs/2505.15726 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Fluctuations of Young diagrams for symplectic groups and semiclassical orthogonal polynomials
Consider an $n\times k$ matrix of i.i.d. Bernoulli random numbers with $p=1/2$. Dual RSK algorithm gives a bijection of this matrix to a pair of Young tableaux of conjugate shape, which is manifestation of skew Howe $GL_{n}\times GL_{k}$-duality. Thus the probability measure on zero-ones matrix leads to the probability measure on Young diagrams proportional to the ratio of the dimension of $GL_{n}\times GL_{k}$-representation and the dimension of the exterior algebra $\bigwedge\left(\mathbb{C}^…

This https://arxiv.org/abs/2505.13647 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On $z^\circ$-ideals and annihilator ideals
For $a\in R$, let $P_a$ denote the intersection of all minimal prime ideals of $R$ containing $a$. An ideal $I$ of a ring $R$ is called a $z^{\circ}$-ideal if $P_a\subseteq I$ for all $a\in I$. In this paper, we first investigate the class of $z^{\circ}$-ideals in non-commutative rings. We provide characterizations of $z^{\circ}$-ideals in 2-by-2 generalized triangular matrix rings, full and upper triangular matrix rings, and semiprime rings. Next, we explore new properties of the lattice $rAnn…

This https://arxiv.org/abs/2402.11229 has been replaced.
initial toot: https://mastoxiv.page/@arX…

Spin dynamics and dark particle in a weak-coupled quantum Ising ladder with $\mathcal{D}_8^{(1)}$ spectrum
Emergent Ising$_h^2$ integrability is anticipated in a quantum Ising ladder composed of two weakly-coupled critical transverse field Ising chains. The system is remarkable for including eight types of massive relativistic particles, with their scattering matrix and mass spectrum characterized by the $\mathcal{D}_8^{(1)}$ Lie algebra. In this article, by computing the spin dynamical structure factors following analytical form factor approach, we clearly identify dispersive single-particle excita…

On $z^\circ$-ideals and annihilator ideals
A. Taherifar
https://arxiv.org/abs/2505.13647 https://arxiv.org/pdf/2505.13647

On $z^\circ$-ideals and annihilator ideals
For $a\in R$, let $P_a$ denote the intersection of all minimal prime ideals of $R$ containing $a$. An ideal $I$ of a ring $R$ is called a $z^{\circ}$-ideal if $P_a\subseteq I$ for all $a\in I$. In this paper, we first investigate the class of $z^{\circ}$-ideals in non-commutative rings. We provide characterizations of $z^{\circ}$-ideals in 2-by-2 generalized triangular matrix rings, full and upper triangular matrix rings, and semiprime rings. Next, we explore new properties of the lattice $rAnn…