Entanglement, noise, and the cumulant expansion

TL;DR

This paper introduces an improved Monte Carlo method leveraging lognormal distribution properties to efficiently compute entanglement entropies in interacting fermion systems, reducing computational complexity and overcoming noise issues.

Contribution

The authors present a simplified, enhanced approach that avoids matrix inversion and extends to higher Rényi entropies, improving accuracy and efficiency in entanglement entropy calculations.

Findings

Successfully computed Rényi entropies for n=2 to 10 in the 1D Hubbard model.

Demonstrated the method's ability to extrapolate to von Neumann and infinite Rényi entropies.

Showed the approach reduces noise and computational complexity in entanglement calculations.

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 R\'enyi entanglement entropy for $n>2$. We test our technique by implementing it in combination with the hybrid Monte Carlo algorithm and calculating the $n=2,3,4, \dots, 10$ R\'enyi entropies of the 1D attractive Hubbard model. We use that data to extrapolate to the von Neumann ($n=1$) and $n\to\infty$ cases.