Entanglement and R\'enyi entropies of (1+1)-dimensional O(3) nonlinear sigma model with tensor renormalization group

• URL: http://arxiv.org/abs/2308.02798v3
• Date: Mon, 18 Sep 2023 22:06:13 GMT
• Title: Entanglement and R\'enyi entropies of (1+1)-dimensional O(3) nonlinear sigma model with tensor renormalization group
• Authors: Xiao Luo, Yoshinobu Kuramashi
• Abstract summary: We investigate the entanglement and R'enyi entropies for the sigma+1-dimensional O(3) nonlinear model. The central charge is determined from the scaling properties of both entropies.
• Score: 5.119573066531286
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate the entanglement and R\'enyi entropies for the (1+1)-dimensional O(3) nonlinear sigma model using the tensor renormalization group method. The central charge is determined from the asymptotic scaling properties of both entropies. We also examine the consistency between the entanglement entropy and the $n$th-order R\'enyi entropy with $n\rightarrow 1$.

Related papers

• Tripartite information of free fermions: a universal entanglement coefficient from the sine kernel [51.56484100374058]
  We study the tripartite information I_3 of free fermions on two-dimensional lattices partitioned into three adjacent strips of width w.<n>We prove that g(z) has a unique zero at z* = 1.3288: modes with k_F w z* violate monogamy of mutual information (g > 0)<n>We verify all predictions on square, triangular, and cubic lattices.
  arXiv  Detail & Related papers  (2026-03-03T15:39:35Z)
• Random matrix prediction of average entanglement entropy in non-Abelian symmetry sectors [0.0]
  We study the average bipartite entanglement entropy of Haar-random pure states in quantum many-body systems with global $mathrmSU(2)$ symmetry.<n>Our analysis uses features of random matrix ensembles and provides a fully analytical treatment for arbitrary spin densities.
  arXiv  Detail & Related papers  (2025-12-28T14:10:16Z)
• Entropic Mirror Descent for Linear Systems: Polyak's Stepsize and Implicit Bias [55.72269695392027]
  This paper focuses on applying entropic mirror descent to solve linear systems.<n>The main challenge for the convergence analysis stems from the unboundedness of the domain.<n>To overcome this without imposing restrictive assumptions, we introduce a variant of Polyak-type stepsizes.
  arXiv  Detail & Related papers  (2025-05-05T12:33:18Z)
• Learning with Norm Constrained, Over-parameterized, Two-layer Neural Networks [54.177130905659155]
  Recent studies show that a reproducing kernel Hilbert space (RKHS) is not a suitable space to model functions by neural networks. In this paper, we study a suitable function space for over- parameterized two-layer neural networks with bounded norms.
  arXiv  Detail & Related papers  (2024-04-29T15:04:07Z)
• Two-dimensional topological paramagnets protected by $\mathbb{Z}_3$ symmetry: Properties of the boundary Hamiltonian [0.0]
  We study gapless edge modes corresponding to $mathbbZ_3$ symmetry-protected topological phases of two-dimensional three-state Potts paramagnets on a triangular lattice. Numerically, we show that low-energy states in the continuous limit of the edge model can be described by conformal field theory.
  arXiv  Detail & Related papers  (2023-12-22T22:31:42Z)
• Measurement-induced phase transition for free fermions above one dimension [46.176861415532095]
  Theory of the measurement-induced entanglement phase transition for free-fermion models in $d>1$ dimensions is developed. Critical point separates a gapless phase with $elld-1 ln ell$ scaling of the second cumulant of the particle number and of the entanglement entropy.
  arXiv  Detail & Related papers  (2023-09-21T18:11:04Z)
• Geometric Neural Diffusion Processes [55.891428654434634]
  We extend the framework of diffusion models to incorporate a series of geometric priors in infinite-dimension modelling. We show that with these conditions, the generative functional model admits the same symmetry.
  arXiv  Detail & Related papers  (2023-07-11T16:51:38Z)
• Rigorous derivation of the Efimov effect in a simple model [68.8204255655161]
  We consider a system of three identical bosons in $mathbbR3$ with two-body zero-range interactions and a three-body hard-core repulsion of a given radius $a>0$.
  arXiv  Detail & Related papers  (2023-06-21T10:11:28Z)
• Average-Case Complexity of Tensor Decomposition for Low-Degree Polynomials [93.59919600451487]
  "Statistical-computational gaps" occur in many statistical inference tasks. We consider a model for random order-3 decomposition where one component is slightly larger in norm than the rest. We show that tensor entries can accurately estimate the largest component when $ll n3/2$ but fail to do so when $rgg n3/2$.
  arXiv  Detail & Related papers  (2022-11-10T00:40:37Z)
• When Random Tensors meet Random Matrices [50.568841545067144]
  This paper studies asymmetric order-$d$ spiked tensor models with Gaussian noise. We show that the analysis of the considered model boils down to the analysis of an equivalent spiked symmetric textitblock-wise random matrix.
  arXiv  Detail & Related papers  (2021-12-23T04:05:01Z)
• Entanglement entropy production in deep inelastic scattering [6.359294579761927]
  Deep inelastic scattering (DIS) samples a part of the wave function of a hadron in the vicinity of the light cone. We show that the resulting entanglement entropy depends on time logarithmically, $mathcal S(t)=1/3 ln(t/tau)$ with $tau = 1/m$ for $1/m le tle (mx)-1$, where $m$ is the proton mass and $x$ is Bjorken $x$.
  arXiv  Detail & Related papers  (2021-10-10T19:05:19Z)
• Tensor network simulation of the (1+1)-dimensional $O(3)$ nonlinear $\sigma$-model with $\theta=\pi$ term [17.494746371461694]
  We perform a tensor network simulation of the (1+1)-dimensional $O(3)$ nonlinear $sigma$-model with $theta=pi$ term. Within the Hamiltonian formulation, this field theory emerges as the finite-temperature partition function of a modified quantum rotor model decorated with magnetic monopoles.
  arXiv  Detail & Related papers  (2021-09-23T12:17:31Z)
• Mean-Square Analysis with An Application to Optimal Dimension Dependence of Langevin Monte Carlo [60.785586069299356]
  This work provides a general framework for the non-asymotic analysis of sampling error in 2-Wasserstein distance. Our theoretical analysis is further validated by numerical experiments.
  arXiv  Detail & Related papers  (2021-09-08T18:00:05Z)
• Symmetry-resolved entanglement entropy in Wess-Zumino-Witten models [0.0]
  We first consider $SU(2)_k$ as a case study and then generalise to an arbitrary non-abelian Lie group. A $loglog L$ contribution to the R'enyi entropies exhibits a universal form related to the underlying symmetry group of the model.
  arXiv  Detail & Related papers  (2021-06-30T09:55:23Z)
• Entanglement Entropy from TFD Entropy Operator [0.0]
  We show that for two-dimensional conformal theories defined in a torus, a choice of moduli space allows the typical entropy operator of the TFD to provide the entanglement entropy. We also propose a model for the evolution of the entanglement entropy and show that it grows linearly with time.
  arXiv  Detail & Related papers  (2020-07-09T13:56:17Z)
• Classical Models of Entanglement in Monitored Random Circuits [0.0]
  We show the evolution of entanglement entropy in quantum circuits composed of Haar-random gates and projective measurements. We also establish a Markov model for the evolution of the zeroth R'enyi entropy and demonstrate that, in one dimension and in the limit of large local dimension, it coincides with the corresponding second-R'enyi-entropy model.
  arXiv  Detail & Related papers  (2020-04-14T18:00:14Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.