Thermalization and light cones in a model with weak integrability breaking

TL;DR

This paper investigates how weak integrability breaking affects the non-equilibrium dynamics of a lattice model of spinless fermions, revealing prethermalization, thermalization timescales, and universal light cone structures.

Contribution

It introduces an equation of motion approach validated against DMRG to analyze weak integrability breaking effects on quantum quenches in fermionic lattice models.

Findings

Observation of prethermalization plateaux at intermediate times

Identification of a universal power-law scaling ($t^{1/3}$) for light cone width

Determination of thermalization crossover times depending on initial conditions

Abstract

We employ equation of motion techniques to study the non-equilibrium dynamics in a lattice model of weakly interacting spinless fermions. Our model provides a simple setting for analyzing the effects of weak integrability breaking perturbations on the time evolution after a quantum quench. We establish the accuracy of the method by comparing results at short and intermediate times to time-dependent density matrix renormalization group computations. For sufficiently weak integrability-breaking interactions we always observe prethermalization plateaux, where local observables relax to non-thermal values at intermediate time scales. At later times a crossover towards thermal behaviour sets in. We determine the associated time scale, which depends on the initial state, the band structure of the non-interacting theory, and the strength of the integrability breaking perturbation. Our method allows us to analyze in some detail the spreading of correlations and in particular the structure of the associated light cones in our model. We find that the interior and exterior of the light cone are separated by an intermediate region, the temporal width of which appears to scale with a universal power-law $t^{1/3}$.