R\'enyi negativities in non-equilibrium open free-boson chains

TL;DR

This paper studies the non-equilibrium dynamics of Re9nyi negativities in open free-boson chains after a quantum quench, combining analytical solutions with numerical verification in a dissipative environment.

Contribution

It provides exact analytical results for the evolution of Re9nyi negativities in dissipative free-boson chains using a hydrodynamic limit and stationary phase method, validated by numerical tests.

Findings

Exact analytical expressions for Re9nyi negativities dynamics

Validation of analytical results with numerical simulations

Identification of quasi-particle picture in weak dissipation limit

Abstract

In this paper, we consider the dynamics of R\'enyi negativities after a quantum quench in the free-boson chain with homogeneous dissipation. Initially we prepare the system in the squeezed thermal state, and then let it evolves under the tight-binding bosonic Hamiltonian with local linear dissipation. We use the Lindblad equation to solve the time evolution of the covariance matrix, from which one can obtain the time dependence of R\'enyi negativities. We are interested in the weak dissipation hydrodynamic limit where a quasi-particle picture emerges. In this limit, exact results of non-equilibrium dynamics of R\'enyi negativities can be obtained using the stationary phase method. We consider the R\'enyi negativities between both adjacent and disjoint regions in a infinite chain. We numerically test our analytical predictions and perfect matches have found.