Symmetry-resolved entanglement in many-body systems

TL;DR

This paper introduces a geometric method to analyze symmetry-resolved entanglement in many-body systems, providing exact results for entanglement measures in 1+1D conformal field theories and applying them to various models.

Contribution

It develops a novel geometric approach using Aharonov-Bohm fluxes to extract symmetry sector contributions to entanglement, with exact results and experimental implications.

Findings

Total entanglement entropy scales as ln L with sector contributions varying by system.

Interacting fermion chains show sqrt(ln L) sector contributions.

Measurements of charge sector entanglement are experimentally feasible.

Abstract

Similarly to the system Hamiltonian, a subsystem's reduced density matrix is composed of blocks characterized by symmetry quantum numbers (charge sectors). We present a geometric approach for extracting the contribution of individual charge sectors to the subsystem's entanglement measures within the replica trick method, via threading appropriate conjugate Aharonov-Bohm fluxes through a multi-sheet Riemann surface. Specializing to the case of 1+1D conformal field theory, we obtain general exact results for the entanglement entropies and spectrum, and apply them to a variety of systems, ranging from free and interacting fermions to spin and parafermion chains, and verify them numerically. We find that the total entanglement entropy, which scales as $\ln L$, is composed of $\sqrt{\ln L}$ contributions of individual subsystem charge sectors for interacting fermion chains, or even $\mathcal{O} (L^0)$ contributions when total spin conservation is also accounted for. We also explain how measurements of the contribution to the entanglement from separate charge sectors can be performed experimentally with existing techniques.