Detecting Symmetry-Resolved Entanglement: A Quantum Monte Carlo Approach

TL;DR

This paper introduces a quantum Monte Carlo method to compute symmetry-resolved entanglement in large-scale interacting quantum systems, enabling analysis of symmetry contributions in complex models.

Contribution

The authors develop a novel QMC approach for symmetry-resolved Rènyi entropies, applicable to higher-dimensional and strongly interacting systems, advancing numerical tools in quantum many-body physics.

Findings

Confirmed conformal-field-theory predictions in 1D TFIM

Observed entanglement equipartition at 2D Ising critical point

Results consistent with expected scaling in 1D Heisenberg chain

Abstract

Symmetry and entanglement are two fundamental concepts in quantum many-body physics. Their interplay is captured by symmetry-resolved entanglement, which decomposes the total entanglement into contributions from different symmetry sectors. Computing symmetry-resolved entanglement in strongly interacting higher-dimensional quantum systems remains challenging. Here, we introduce a quantum Monte Carlo (QMC) approach for computing symmetry-resolved R\'enyi entropies (SRRE) in large-scale interacting systems by measuring disorder (symmetry-twisted) operators on replica manifolds and reconstructing SRRE from the corresponding charged moments. We apply this method to the transverse-field Ising model (TFIM) in one and two dimensions. In one dimension, we recover the conformal-field-theory prediction for the logarithmic scaling of the disorder operator and observe the expected approach to entanglement equipartition. In two dimensions, our data provide numerical evidence consistent with entanglement equipartition at the (2+1)D Ising critical point. We further apply the framework to the 1D Heisenberg chain and obtain results consistent with the expected asymptotic scaling and finite-size corrections in the U(1)-resolved sectors. Our work establishes a practical numerical route to symmetry-resolved entanglement in interacting lattice models and provides a useful framework for future studies beyond one dimension.