Quantum quenches and thermalization in one-dimensional fermionic systems

TL;DR

This paper investigates how strongly correlated fermions in one-dimensional lattices relax and thermalize after a quantum quench, revealing differences in dynamics between fermions and bosons and the impact of integrability.

Contribution

It provides a detailed analysis of the relaxation dynamics of fermionic observables post-quench, highlighting the role of integrability and off-diagonal matrix elements in thermalization.

Findings

N(k) thermalizes similarly for fermions and bosons.

n(k) exhibits slower relaxation in fermionic systems.

Thermalization breaks down near the integrable point.

Abstract

We study the dynamics and thermalization of strongly correlated fermions in finite one-dimensional lattices after a quantum quench. Our calculations are performed using exact diagonalization. We focus on one- and two-body observables such as the momentum distribution function [n(k)] and the density-density structure factor [N(k)], respectively, and study the effects of approaching an integrable point. We show that while the relaxation dynamics and thermalization of N(k) for fermions is very similar to the one of hardcore bosons, the behavior of n(k) is distinctively different. The latter observable exhibits a slower relaxation dynamics in fermionic systems. We identify the origin of this behavior, which is related to the off-diagonal matrix elements of n(k) in the basis of the eigenstates of the Hamiltonian. More generally, we find that thermalization occurs far away from integrability and that it breaks down as one approaches the integrable point.