Non-adiabatic dynamics of the entanglement entropy in a symmetry-breaking Haldane insulator

TL;DR

This paper investigates the non-adiabatic behavior of entanglement entropy in a symmetry-breaking Haldane insulator, revealing a critical regime where entanglement is robust despite symmetry breaking.

Contribution

It demonstrates how entanglement dynamics can be predicted near a critical point using a two-level model, challenging the notion that symmetry-protected topological phases are fragile.

Findings

Gap closes at a critical point under symmetry breaking.

Adiabatic evolution fails at the critical point.

Entanglement measurement remains robust near the critical regime.

Abstract

We study the non-adiabatic dynamics of a typical symmetry-protected topological phase-the Haldane insulator phase with broken bond-centered inversion. By continuously breaking the middle chain, we find the gap closes at a critical point in the deep Haldane insulator regime with a change of particle number partition of the left or right system. The adiabatic evolution fails at this critical point and we show how to predict the dynamics of the entanglement entropy near this point using a two-level model. These results show that one can find a critical regime where the entanglement measurement is relatively robust against perturbation that breaks the protecting symmetries in the Haldane insulator. This is in contrast to the common belief that the symmetry-protected topological phases are fragile without the protecting symmetries.