Wang-Landau method for calculating Rényi entropies in finite-temperature quantum Monte Carlo simulations

2012/07/30 by Stephen Inglis, Roger G. Melko · 4 citations
Physics and Astronomy · #Physics of Superconductivity and Magnetism #Quantum many-body systems #Theoretical and Computational Physics #cond-mat.stat-mech #cond-mat.str-el #quant-ph

paper · pdf · doi:10.1103/physreve.87.013306

published as Phys. Rev. E 87, 013306 (2013) · 9 pages, 7 figures

arxiv created 2012/07/30 · openalex publication_date 2013/01/22 · arxiv updated 2013/01/23 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We implement a Wang-Landau sampling technique in quantum Monte Carlo (QMC) simulations for the purpose of calculating the Rényi entanglement entropies and associated mutual information. The algorithm converges an estimate for an analog to the density of states for stochastic series expansion QMC, allowing a direct calculation of Rényi entropies without explicit thermodynamic integration. We benchmark results for the mutual information on two-dimensional (2D) isotropic and anisotropic Heisenberg models, a 2D transverse field Ising model, and a three-dimensional Heisenberg model, confirming a critical scaling of the mutual information in cases with a finite-temperature transition. We discuss the benefits and limitations of broad sampling techniques compared to standard importance sampling methods.

Citations

• Stochastic series expansion method for quantum Ising models with arbitrary interactions
• A generalization of Handscomb's quantum Monte Carlo scheme-application to the 1D Hubbard model
• Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition

Cited by

• Nonconvergence of the Wang-Landau algorithms with multiple random walkers
• Critical scaling of the mutual information in two-dimensional disordered Ising models
• Path-integral Monte Carlo method for Rényi entanglement entropies
• Geometrical mutual information at the tricritical point of the two-dimensional Blume–Capel model

Related

• Tracking the variation of entanglement Rényi negativity: a quantum Monte Carlo study
• Bipartite reweight-annealing algorithm of quantum Monte Carlo to extract large-scale data of entanglement entropy and its derivative
• Quantum algorithm for Wang-Landau sampling
• Calculating Thermodynamics Properties of Quantum Systems by a non-Markovian Monte Carlo Procedure
• High-efficiency quantum Monte Carlo algorithm for extracting entanglement entropy in interacting fermion systems