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

Abstract

We implement a Wang-Landau sampling technique in quantum Monte Carlo (QMC) for the purpose of calculating the Renyi entanglement entropies and associated mutual information. The algorithm converges an estimate for an analogue to the density of states for Stochastic Series Expansion QMC allowing a direct calculation of Renyi entropies without explicit thermodynamic integration. We benchmark results for the mutual information on two-dimensional (2D) isotropic and anisotropic Heisenberg models, 2D transverse field Ising model, and 3D 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.

9 pages, 7 figures

References in corpus (9)

• Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum
• Entanglement Entropy in the O(N) model
• Stochastic series expansion method for quantum Ising models with arbitrary interactions
• Entanglement entropy of critical spin liquids
• Numerical study of entanglement entropy in SU(2) lattice gauge theory
• Finite Size Scaling of Mutual Information: A Scalable Simulation
• Finite Temperature Critical Behavior of Mutual Information
• Analysis of the convergence of the 1/t and Wang-Landau algorithms in the calculation of multidimensional integrals
• Optimized Broad-Histogram Ensembles for the Simulation of Quantum Systems

Cited by in corpus (15)

• Scaling of entanglement entropy at deconfined quantum criticality
• Entanglement entropy scaling in the bilayer Heisenberg spin system
• Measuring Rényi entanglement entropy with high efficiency and precision in quantum Monte Carlo simulations
• Improving entanglement and thermodynamic Rényi entropy measurements in quantum Monte Carlo
• Fermion disorder operator at Gross-Neveu and deconfined quantum criticalities
• A path integral Monte Carlo method for Rényi entanglement entropies
• Unlocking the general relationship between energy and entanglement spectra via the wormhole effect
• Incremental SWAP Operator for Entanglement Entropy: Application for Exponential Observables in Quantum Monte Carlo Simulation
• Non-equilibrium quantum Monte Carlo algorithm for stabilizer Renyi entropy in spin systems
• On the entanglement across a cubic interface in 3+1 dimensions
• Different temperature-dependence for the edge and bulk of entanglement Hamiltonian
• A Path Integral Ground State Monte Carlo Algorithm for Entanglement of Lattice Bosons
• Rényi Information flow in the Ising model with single-spin dynamics
• Reducing autocorrelation time in determinant quantum Monte Carlo using Wang-Landau algorithm: application to Holstein model
• Rényi entropy of quantum anharmonic chain at non-zero temperature