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Physica A Statistical Mechanics and its Applications

Topological phase transition in the two-dimensional anisotropic Heisenberg model: A study using the Replica Exchange Wang–Landau sampling

T. P. Figueiredo, J. C. S. Rocha, B. V. Costa

Published Jul 19, 2017• 6 citations
Publisher
DOI
10.1016/j.physa.2017.07.010

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In this paper, we use the Replica-Exchange Wang–Landau (REWL) technique to study the behavior of the two-point correlation function of the site diluted classical anisotropic Heisenberg (AH) model in two dimensions. The model has a topological Berezinskii–Kosterlitz–Thouless (BKT) transition for any dilution down to the percolation threshold, [Formula: see text]. Contrary to earlier results that predict the exponent of the correlation function, [Formula: see text], to decay linearly to zero as a function of temperature, we found that it decreases with temperature to a finite value [Formula: see text] at [Formula: see text] for any dilution [Formula: see text].
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.