Charge-resolved entanglement in the presence of topological defects

TL;DR

This paper investigates how topological defects like solitons influence symmetry-resolved entanglement entropy in the Su-Schrieffer-Heeger model, revealing richer entanglement structures and conditions for equipartition involving zero modes and defect configurations.

Contribution

It provides the first detailed analysis of charge-resolved entanglement in the presence of topological defects, combining exact, asymptotic, and numerical methods.

Findings

Richer entanglement structure due to defects

Charge splitting enhances entanglement in certain sectors

Equipartition depends on defect inclusion and zero mode occupation

Abstract

Topological excitations or defects such as solitons are ubiquitous throughout physics, supporting numerous interesting phenomena like zero energy modes with exotic statistics and fractionalized charges. In this paper, we study such objects through the lens of symmetry-resolved entanglement entropy. Specifically, we compute the charge-resolved entanglement entropy for a single interval in the low-lying states of the Su-Schrieffer-Heeger model in the presence of topological defects. Using a combination of exact and asymptotic analytical techniques, backed up by numerical analysis, we find that, compared to the unresolved counterpart and to the pure system, a richer structure of entanglement emerges. This includes a redistribution between its configurational and fluctuational parts due to the presence of the defect and an interesting interplay with entanglement equipartition. In particular, in a subsystem that excludes the defect, equipartition is restricted to charge sectors of the same parity, while full equipartition is restored if the subsystem includes the defect, as long as the associated zero mode remains unoccupied. Additionally, by exciting zero modes in the presence of multiple defects, we observe a significant enhancement of entanglement in certain charge sectors, due to charge splitting on the defects. The two different scenarios featuring the breakdown of entanglement equipartition are underlied by a joint mechanism, which we unveil by relating them to degeneracies in the spectrum of the entanglement Hamiltonian. In addition, equipartition is shown to stem from an equidistant entanglement spectrum.