Entanglement Hamiltonians in dissipative free fermions and the time-dependent GGE

TL;DR

This paper explores how entanglement Hamiltonians evolve in dissipative free-fermionic systems, revealing a universal time-dependent GGE structure in long-time, weak-dissipation regimes, grounded in a quasiparticle framework.

Contribution

It introduces a quasiparticle-based operator formulation to explicitly derive the entanglement Hamiltonian and demonstrates its universal t-GGE form in dissipative free fermions.

Findings

Entanglement Hamiltonian follows a universal time-dependent GGE form.

Explicit expressions for EH at the ballistic scale are derived.

The quasiparticle picture explains the emergence of the t-GGE.

Abstract

We investigate the dynamics of Entanglement Hamiltonians (EHs) in dissipative free-fermionic systems using a recent operator-based formulation of the quasiparticle picture. Focusing on gain and loss dissipation, we study the post-quench evolution and derive explicit expressions for the EH at the ballistic scale. In the long-time and weak-dissipation regime, the EH is shown to take the form of a time-dependent Generalized Gibbs Ensemble (t-GGE), with a structure that is universal across different initial states of the quench protocol. Within this framework, the emergence of the t-GGE is fully accounted for by the quasiparticle picture, and we argue that this description remains valid whenever the Lindbladian admits an appropriate coarse-grained representation.