Exact quench dynamics of symmetry resolved entanglement in a free fermion chain

TL;DR

This paper provides an exact analysis of the time evolution of symmetry-resolved entanglement and mutual information in a free fermion chain, revealing time delays, equipartition, and growth behaviors linked to quasiparticle dynamics.

Contribution

It extends previous work by deriving exact results for symmetry-resolved entanglement dynamics, including mutual information, in free fermion systems and introduces a symmetry-resolved mutual information measure.

Findings

Entanglement entropies show a charge-dependent time delay.

Effective equipartition of entanglement occurs at large times and sizes.

Number entropy grows logarithmically before saturation.

Abstract

The study of the entanglement dynamics plays a fundamental role in understanding the behaviour of many-body quantum systems out of equilibrium. In the presence of a globally conserved charge, further insights are provided by the knowledge of the resolution of entanglement in the various symmetry sectors. Here, we carry on the program we initiated in [Phys. Rev. B 103, L041104 (2021)], for the study of the time evolution of the symmetry resolved entanglement in free fermion systems. We complete and extend our derivations also by defining and quantifying a symmetry resolved mutual information. The entanglement entropies display a time delay that depends on the charge sector that we characterise exactly. Both entanglement entropies and mutual information show effective equipartition in the scaling limit of large time and subsystem size. Furthermore, we argue that the behaviour of the charged entropies can be quantitatively understood in the framework of the quasiparticle picture for the spreading of entanglement, and hence we expect that a proper adaptation of our results should apply to a large class of integrable systems. We also find that the number entropy grows logarithmically with time before saturating to a value proportional to the logarithm of the subsystem size.