Dynamics of entanglement asymmetry for space-inversion symmetry of free fermions on honeycomb lattices

TL;DR

This paper investigates how entanglement asymmetry in free fermions on a honeycomb lattice depends on energy imbalance and how it evolves after a quench, revealing persistent symmetry breaking linked to flat bands.

Contribution

It uncovers the nonanalytic behavior of entanglement asymmetry due to Dirac points and shows conditions where symmetry breaking persists after a quench.

Findings

Entanglement asymmetry exhibits nonanalytic dependence on energy imbalance.

Post-quench, entanglement asymmetry can relax to a finite value, indicating persistent symmetry breaking.

Flat energy dispersion prevents symmetry restoration in certain conditions.

Abstract

We study the entanglement asymmetry for the space-inversion symmetry of free fermions on a two-dimensional honeycomb lattice with an on-site energy imbalance between the two sublattices. We show that the entanglement asymmetry of a local subsystem exhibits nonanalytic dependence on the energy imbalance, due to the presence of Dirac points in the Brillouin zone. We also study the quench dynamics from the ground state into the inversion-symmetric point at which the energy imbalance vanishes. Under certain conditions on the subsystem geometry, the entanglement asymmetry relaxes to a finite value after the quench, revealing that the inversion-symmetry breaking in the initial ground state can persist even under the symmetric dynamics. We attribute the absence of symmetry restoration to the presence of a flat energy dispersion (flat band) in a specific direction.