Resummation-based Quantum Monte Carlo for Entanglement Entropy Computation

TL;DR

The paper introduces ResumEE, an efficient quantum Monte Carlo algorithm that significantly improves the computation of entanglement entropy in SU(N) spin models, enabling high-accuracy analysis of complex quantum phases.

Contribution

It develops ResumEE, a novel resummation-based Monte Carlo method that exponentially accelerates entanglement entropy calculations for SU(N) models, especially for continuous N.

Findings

ResumEE outperforms previous estimators in 1D and 2D SU(2) systems.

It accurately detects entanglement scaling at the Nèel-to-VBS transition.

The method provides reliable access to conformal field theory data in highly entangled quantum matter.

Abstract

Based on the recently developed resummation-based quantum Monte Carlo method for the SU($N$) spin and loop-gas models, we develop a new algorithm, dubbed ResumEE, to compute the entanglement entropy (EE) with greatly enhanced efficiency. Our ResumEE exponentially speeds up the computation of the exponentially small value of the $\langle e^{-S^{(2)}}\rangle$, where $S^{(2)}$ is the 2nd order R\'enyi EE, such that the $S^{(2)}$ for a generic 2D quantum SU($N$) spin models can be readily computed with high accuracy. We benchmark our algorithm with the previously proposed estimators of $S^{(2)}$ on 1D and 2D SU($2$) Heisenberg spin systems to reveal its superior performance and then use it to detect the entanglement scaling data of the N\'eel-to-VBS transition on 2D SU($N$) Heisenberg model with continuously varying $N$. Our ResumEE algorithm is efficient for precisely evaluating the entanglement entropy of SU($N$) spin models with continuous $N$ and reliable access to the conformal field theory data for the highly entangled quantum matter.