Dynamics of charge-imbalance-resolved entanglement negativity after a quench in a free-fermion model

TL;DR

This paper investigates how charge-imbalance-resolved entanglement negativity evolves over time after a quench in free-fermion systems, revealing equipartition properties and proposing a general dynamical formula.

Contribution

It introduces the study of charge-imbalance-resolved negativity dynamics post-quench and proposes a conjecture for its formula, extending symmetry-resolved entanglement analysis.

Findings

Charge-imbalance-resolved negativity exhibits effective equipartition at large times.

Early and infinite times show perfect equipartition.

A conjectured formula for the dynamics of charged Rénnyi negativities is proposed.

Abstract

The presence of a global internal symmetry in a quantum many-body system is reflected in the fact that the entanglement between its subparts is endowed with an internal structure, namely it can be decomposed as sum of contributions associated to each symmetry sector. The symmetry resolution of entanglement measures provides a formidable tool to probe the out-of-equilibrium dynamics of quantum systems. Here, we study the time evolution of charge-imbalance-resolved negativity after a global quench in the context of free-fermion systems, complementing former works for the symmetry-resolved entanglement entropy. We find that the charge-imbalance-resolved logarithmic negativity shows an effective equipartition in the scaling limit of large times and system size, with a perfect equipartition for early and infinite times. We also derive and conjecture a formula for the dynamics of the charged R\'enyi logarithmic negativities. We argue that our results can be understood in the framework of the quasiparticle picture for the entanglement dynamics, and provide a conjecture that we expect to be valid for generic integrable models.