Symmetry resolved entanglement in gapped integrable systems: a corner transfer matrix approach

TL;DR

This paper investigates symmetry-resolved entanglement in gapped integrable models using corner transfer matrix techniques, providing exact formulas and numerical validation for both free and interacting systems.

Contribution

It introduces an exact correlation matrix approach for symmetry-resolved entanglement in gapped systems, applicable to both free and interacting models, with analytical and numerical results.

Findings

Exact expressions for charged moments and symmetry-resolved entropies.

Equipartition of entanglement in the XXZ spin chain.

Limited equipartition in the harmonic chain, depending on limits.

Abstract

We study the symmetry resolved entanglement entropies in gapped integrable lattice models. We use the corner transfer matrix to investigate two prototypical gapped systems with a U(1) symmetry: the complex harmonic chain and the XXZ spin-chain. While the former is a free bosonic system, the latter is genuinely interacting. We focus on a subsystem being half of an infinitely long chain. In both models, we obtain exact expressions for the charged moments and for the symmetry resolved entropies. While for the spin chain we found exact equipartition of entanglement (i.e. all the symmetry resolved entropies are the same), this is not the case for the harmonic system where equipartition is effectively recovered only in some limits. Exploiting the gaussianity of the harmonic chain, we also develop an exact correlation matrix approach to the symmetry resolved entanglement that allows us to test numerically our analytic results.