Post-quench relaxation dynamics of Gross-Neveu lattice fermions

TL;DR

This paper investigates the relaxation dynamics of a 1D lattice Gross-Neveu model after a parameter quench, revealing how the system approaches equilibrium or a GGE depending on system size and reservoir coupling.

Contribution

It provides a numerical analysis of post-quench relaxation in the lattice Gross-Neveu model, highlighting the roles of system size, reservoir coupling, and the applicability of ETH and GGE.

Findings

Order parameter oscillates and revives in finite systems after a quench.

In the thermodynamic limit, the order parameter reaches a stationary value consistent with ETH.

Finite-momentum correlations equilibrate only with non-zero reservoir coupling.

Abstract

We study the quantum relaxation dynamics for a lattice version of the one-dimensional (1D) $N$-flavor Gross-Neveu (GN) model after a Hamiltonian parameter quench. Allowing for a system-reservoir coupling $\gamma$, we numerically describe the system dynamics through a time-dependent self-consistent Lindblad master equation. For a closed ($\gamma=0$) finite-size system subjected to an interaction parameter quench, the order parameter dynamics exhibits oscillations and revivals. In the thermodynamic limit, our results imply that the order parameter reaches its post-quench stationary value in accordance with the eigenstate thermalization hypothesis (ETH). However, time-dependent finite-momentum correlation matrix elements equilibrate only if $\gamma>0$. Our findings are consistent with the system being described by a pertinent Generalized Gibbs Ensemble (GGE) and, accordingly, highlight subtle yet important aspects of the post-quench relaxation dynamics of quantum many-body systems.