Entanglement entropy from non-equilibrium Monte Carlo simulations

Abstract

We study the entanglement entropy in lattice field theory using a simulation algorithm based on Jarzynski's theorem. We focus on the entropic c-function for the Ising model in two and in three dimensions: after validating our algorithm against known analytical results from conformal field theory in two dimensions, we present novel results for the three-dimensional case. We show that our algorithm, which is highly parallelized on graphics processing units, allows one to precisely determine the subleading corrections to the area law, which have been investigated in many recent works. Possible generalizations of this study to other strongly coupled theories are discussed.

arXiv comment1+33 pages; v2: typos corrected, matches published version

References in corpus (79)

• Quantum entanglement
• Gauge Theory Correlators from Non-Critical String Theory
• A nonequilibrium equality for free energy differences
• Concentrating Partial Entanglement by Local Operations
• Area laws for the entanglement entropy - a review
• Entanglement in quantum critical phenomena
• The Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences
• Topological entanglement entropy
• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• Aspects of Holographic Entanglement Entropy
• Dynamical Ensembles in Nonequilibrium Statistical Mechanics
• Entanglement in a simple quantum phase transition
• Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems
• Equilibrium free energy differences from nonequilibrium measurements: a master equation approach
• Building up spacetime with quantum entanglement
• The information paradox: A pedagogical introduction
• Bounding scalar operator dimensions in 4D CFT
• Dynamical ensembles in stationary states
• Quantum entanglement in condensed matter systems
• Fluctuation-Dissipation: Response Theory in Statistical Physics
• Entanglement monotones
• Solving the 3D Ising Model with the Conformal Bootstrap
• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• Thermalization and prethermalization in isolated quantum systems: a theoretical overview
• Entanglement negativity in quantum field theory
• Entanglement as a Probe of Confinement
• Measuring Renyi Entanglement Entropy with Quantum Monte Carlo
• A finite entanglement entropy and the c-theorem
• On the RG running of the entanglement entropy of a circle
• Topological Order and Conformal Quantum Critical Points
• Form factors of branch-point twist fields in quantum integrable models and entanglement entropy
• Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum
• Rare events and the convergence of exponentially averaged work values
• Entanglement negativity in extended systems: A field theoretical approach
• A refinement of entanglement entropy and the number of degrees of freedom
• Information Loss
• Entanglement entropy in gauge theories and the holographic principle for electric strings
• Pushing the Limits of Monte Carlo Simulations for the 3d Ising Model
• Shannon and entanglement entropies of one- and two-dimensional critical wave functions
• AdS Bubbles, Entropy and Closed String Tachyons
• Jarzynski-like equality for the out-of-time-ordered correlator
• The quasiprobability behind the out-of-time-ordered correlator
• Markov property of the CFT vacuum and the a-theorem
• A c-theorem for the entanglement entropy
• Entanglement Entropy and Twist Fields
• Entanglement entropy of two disjoint blocks in critical Ising models
• Unusual Corrections to Scaling in Entanglement Entropy
• Quantum Monte Carlo calculation of entanglement Renyi entropies for generic quantum systems
• Numerical study of entanglement entropy in SU(2) lattice gauge theory
• Critical exponents of the 3d Ising and related models from Conformal Bootstrap
• Rényi entropy and conformal defects
• Thermodynamics of quantum information scrambling
• On Rényi entropies of disjoint intervals in conformal field theory
• Rényi entropy of a line in two-dimensional Ising models
• Confinement, Phase Transitions and non-Locality in the Entanglement Entropy
• Entanglement negativity and conformal field theory: a Monte Carlo study
• Entanglement scaling in two-dimensional gapless systems
• Entanglement entropy from nonequilibrium work
• Work Statistics, Loschmidt Echo and Information Scrambling in Chaotic Quantum Systems
• QCD thermodynamics from lattice calculations with non-equilibrium methods: The SU(3) equation of state
• Entanglement at a Two-Dimensional Quantum Critical Point: a T=0 Projector Quantum Monte Carlo Study
• Out-of-equilibrium protocol for Rényi entropies via the Jarzynski equality
• Is entanglement a probe of confinement?
• Finite-size corrections of the Entanglement Entropy of critical quantum chains
• GPU-based Swendsen-Wang multi-cluster algorithm for the simulation of two-dimensional classical spin systems
• Entanglement in Four-Dimensional SU(3) Gauge Theory
• Entanglement in gapless resonating valence bond states
• A note on the 3D Ising model as a string theory
• Lattice study of Rényi entanglement entropy in $SU(N_c)$ lattice Yang-Mills theory with $N_c=2,3,4$
• Scaling of entanglement in $2+1$-dimensional scale-invariant field theories
• Unusual Corrections to Scaling and Convergence of Universal Renyi Properties at Quantum Critical Points
• Toward a 3d Ising model with a weakly-coupled string theory dual
• CUDA programs for GPU computing of Swendsen-Wang multi-cluster spin flip algorithm: 2D and 3D Ising, Potts, and XY models
• Universal entanglement and correlation measure in two-dimensional conformal field theories
• Strong coupling from non-equilibrium Monte Carlo simulations
• On the Entanglement Entropy of Maxwell Theory: A Condensed Matter Perspective
• The 3d Ising Model represented as Random Surfaces
• Holographic spacetime from lattice Yang-Mills theory
• Universal divergence of the Renyi entropy of a thinly sliced torus at the Ising fixed point

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• Duality transformations and the entanglement entropy of gauge theories
• Numerical determination of the width and shape of the effective string using Stochastic Normalizing Flows
• Deep learning lattice gauge theories
• Scaling of Stochastic Normalizing Flows in $\mathrm{SU}(3)$ lattice gauge theory
• Flow-Based Sampling for Entanglement Entropy and the Machine Learning of Defects
• Rényi entanglement entropy of spin chain with Generative Neural Networks
• Resummation-based Quantum Monte Carlo for Entanglement Entropy Computation
• Universal term of Entanglement Entropy in the $\pi$-flux Hubbard model
• Scaling flow-based approaches for topology sampling in $\mathrm{SU}(3)$ gauge theory
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