Measuring Renyi Entanglement Entropy with Quantum Monte Carlo

TL;DR

This paper introduces a quantum Monte Carlo method in the valence bond basis to efficiently measure Renyi entanglement entropy in many-body quantum systems, demonstrating its effectiveness on Heisenberg models.

Contribution

It presents a novel Monte Carlo procedure using a Swap operator to compute Renyi entanglement entropy with improved convergence and applicability to large systems.

Findings

Successfully computed Renyi entropy for a Heisenberg chain with exact agreement.

Confirmed the area law scaling of entanglement entropy in a 2D Heisenberg model.

Demonstrated polynomial-time convergence of the entropy estimation.

Abstract

We develop a quantum Monte Carlo procedure, in the valence bond basis, to measure the Renyi entanglement entropy of a many-body ground state as the expectation value of a unitary {\it Swap} operator acting on two copies of the system. An improved estimator involving the ratio of {\it Swap} operators for different subregions enables simulations to converge the entropy in a time polynomial in the system size. We demonstrate convergence of the Renyi entropy to exact results for a Heisenberg chain. Finally, we calculate the scaling of the Renyi entropy in the two-dimensional Heisenberg model and confirm that the N\'eel groundstate obeys the expected area law for systems up to linear size L=28.