Improving entanglement and thermodynamic R\'enyi entropy measurements in quantum Monte Carlo

TL;DR

This paper introduces an improved quantum Monte Carlo method for measuring entanglement and thermodynamic R'enyi entropies by leveraging participation R'enyi entropies, enabling more accurate and comprehensive entanglement analysis.

Contribution

The authors develop a novel approach linking entanglement and participation R'enyi entropies, enhancing measurement accuracy and enabling thermodynamic entropy estimation in quantum Monte Carlo simulations.

Findings

Enhanced estimators significantly improve entanglement R'enyi entropy measurements.

Method allows high-accuracy thermodynamic R'enyi entropy calculations.

Potential for testing entanglement Hamiltonians against thermal entropy data.

Abstract

We present a method for improving measurements of the entanglement R\'enyi entropies in quantum Monte Carlo simulations by relating them with measurements of participation R\'enyi entropies. Exploiting the capability of building improved estimators for the latter allows to obtain very good estimates for entanglement R\'enyi entropies. When considering a full system instead of a bipartition, the method can be further ameliorated providing access to the thermodynamic R\'enyi entropies with high accuracy. We also explore a recently-proposed method for the reconstruction of the entanglement spectrum from entanglement R\'enyi entropies and finally show how potential entanglement Hamiltonians may be tested for their validity using a comparison with thermal R\'enyi entropies.