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.

arXiv comment9 pages, 7 figures

References in corpus (26)

• Entanglement Entropy and Quantum Field Theory
• An efficient, multiple range random walk algorithm to calculate the density of states
• Entanglement in quantum critical phenomena
• Topological entanglement entropy
• Detecting topological order in a ground state wave function
• Geometric and Renormalized Entropy in Conformal Field Theory
• Quantum Monte Carlo with Directed Loops
• Stochastic series expansion method with operator-loop update
• Measuring Renyi Entanglement Entropy with Quantum Monte Carlo
• Quasi-particle Statistics and Braiding from Ground State Entanglement
• Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum
• The Loop Algorithm
• Bond-order-wave phase and quantum phase transitions in the one-dimensional extended Hubbard model
• Entanglement Entropy in the O(N) model
• Stochastic series expansion method for quantum Ising models with arbitrary interactions
• Entanglement entropy of critical spin liquids
• Quantum Monte Carlo calculation of entanglement Renyi entropies for generic quantum systems
• Numerical study of entanglement entropy in SU(2) lattice gauge theory
• Wang-Landau sampling for quantum systems: algorithms to overcome tunneling problems and calculate the free energy
• Critical temperature and the transition from quantum to classical order parameter fluctuations in the three-dimensional Heisenberg antiferromagnet
• Topological Entanglement Entropy of Z2 Spin liquids and Lattice Laughlin states
• Finite Size Scaling of Mutual Information: A Scalable Simulation
• Quantum Monte Carlo in the Interaction Representation --- Application to a Spin-Peierls Model
• 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 (31)

• Scaling of entanglement entropy at deconfined quantum criticality
• Entanglement negativity via replica trick: a Quantum Monte Carlo approach
• Entanglement entropy scaling in the bilayer Heisenberg spin system
• Nonzero temperature Entanglement Negativity of quantum spin models: Area law, Linked Cluster Expansions and Sudden Death
• First-order phase transition and tricritical scaling behavior of the Blume-Capel model: a Wang-Landau sampling approach
• Measuring Rényi entanglement entropy with high efficiency and precision in quantum Monte Carlo simulations
• Entanglement entropy from nonequilibrium work
• Improving entanglement and thermodynamic Rényi entropy measurements in quantum Monte Carlo
• Detecting Classical Phase Transitions with Renyi Mutual Information
• Fermion disorder operator at Gross-Neveu and deconfined quantum criticalities
• Out-of-equilibrium protocol for Rényi entropies via the Jarzynski equality
• A path integral Monte Carlo method for Rényi entanglement entropies
• Detecting Goldstone Modes with Entanglement Entropy
• A hybrid Monte Carlo approach to the entanglement entropy of interacting fermions
• Unlocking the general relationship between energy and entanglement spectra via the wormhole effect
• Measuring von Neumann entanglement entropies without wave functions
• Entanglement and classical fluctuations at finite-temperature critical points
• Entanglement, noise, and the cumulant expansion
• 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
• On the non-convergence of the Wang-Landau algorithms with multiple random walkers
• Different temperature-dependence for the edge and bulk of entanglement Hamiltonian
• Critical scaling of the mutual information in two-dimensional disordered Ising models
• The entanglement spectrum and Rényi entropies of non-relativistic conformal fermions
• Geometrical mutual information at the tricritical point of the two-dimensional Blume-Capel model
• A Path Integral Ground State Monte Carlo Algorithm for Entanglement of Lattice Bosons
• Rényi Information flow in the Ising model with single-spin dynamics
• Entanglement of Free Fermions and Bosons at Finite Temperature
• 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