Dynamics of charge imbalance resolved negativity after a global quench in free scalar field theory

TL;DR

This paper investigates how charge imbalance resolved negativity evolves over time after a global quench in a 1+1 dimensional free scalar field theory, using analytical and numerical methods for different quench types.

Contribution

It provides analytical formulas for the time evolution of charge imbalance resolved negativity after global quenches in free scalar field theory, supported by numerical tests.

Findings

Analytical expressions for negativity evolution after boundary state quench.

Numerical validation of formulas in lattice models.

Insights into quasi-particle interpretation of the results.

Abstract

In this paper, we consider the time evolution of charge imbalance resolved negativity after a global quench in the 1+1 dimensional complex Klein-Gordon theory. We focus on two types of global quenches which are called boundary state quench and mass quench respectively. We first study the boundary state quench where the post-quench dynamic is governed by a massless Hamiltonian. In this case, the temporal evolution of charged imbalance resolved negativity can be obtained first by evaluating the correlators of the fluxed twist field in the upper half plane and then applying Fourier transformation. We numerical test our analytical formulas in the underlying lattice model. We also study the mass quench in the complex harmonic chain where the system is evolved according to a massive Hamiltonian after the quench. We argue that our results can be understood in the framework of quasi-particle picture.