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arXiv · 1508.04375

Entanglement, noise, and the cumulant expansion

Joaquín E. Drut·William J. Porter
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Abstract

We put forward a simpler and improved variation of a recently proposed method to overcome the signal-to-noise problem found in Monte Carlo calculations of the entanglement entropy of interacting fermions. The present method takes advantage of the approximate lognormal distributions that characterize the signal-to-noise properties of other approaches. In addition, we show that a simple rewriting of the formalism allows circumvention of the inversion of the restricted one-body density matrix in the calculation of the $n$-th Rényi entanglement entropy for $n>2$. We test our technique by implementing it in combination with the hybrid Monte Carlo algorithm and calculating the $n=2,3,4, \dots, 10$ Rényi entropies of the 1D attractive Hubbard model. We use that data to extrapolate to the von Neumann ($n=1$) and $n\to\infty$ cases.

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Joaquín E. Drut, William J. Porter. 2016-02-09. Entanglement, noise, and the cumulant expansion. https://doi.org/10.1103/physreve.93.043301

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