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arXiv · 1506.06654

A hybrid Monte Carlo approach to the entanglement entropy of interacting fermions

Joaquín E. Drut·William J. Porter
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Abstract

The Monte Carlo calculation of Rényi entanglement entropies $S^{}_n$ of interacting fermions suffers from a well-known signal-to-noise problem, even for a large number of situations in which the infamous sign problem is absent. A few methods have been proposed to overcome this issue, such as ensemble switching and the use of auxiliary partition-function ratios. Here, we present an approach that builds on the recently proposed free-fermion decomposition method; it incorporates entanglement in the probability measure in a natural way; it takes advantage of the hybrid Monte Carlo algorithm (an essential tool in lattice quantum chromodynamics and other gauge theories with dynamical fermions); and it does not suffer from noise problems. This method displays no sign problem for the same cases as other approaches and is therefore useful for a wide variety of systems. As a proof of principle, we calculate $S_2^{}$ for the one-dimensional, half-filled Hubbard model and compare with results from exact diagonalization and the free-fermion decomposition method.

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Joaquín E. Drut, William J. Porter. 2015-10-10. A hybrid Monte Carlo approach to the entanglement entropy of interacting fermions. https://doi.org/10.1103/physrevb.92.125126

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