Interaction Quench in the Hubbard model

TL;DR

This paper investigates the real-time dynamics of a Hubbard model after a sudden interaction quench, revealing three distinct regimes from initial correlation buildup to eventual thermalization, using the flow equation method.

Contribution

It introduces a systematic analysis of nonequilibrium dynamics in the Hubbard model post-quench, identifying three characteristic time regimes and their physical descriptions.

Findings

Identification of three distinct time regimes in the quench dynamics.

Demonstration of thermalization with a temperature proportional to interaction strength.

Application of the flow equation method to study real-time evolution.

Abstract

Motivated by recent experiments in ultracold atomic gases that explore the nonequilibrium dynamics of interacting quantum many-body systems, we investigate the opposite limit of Landau's Fermi liquid paradigm: We study a Hubbard model with a sudden interaction quench, that is the interaction is switched on at time t=0. Using the flow equation method, we are able to study the real time dynamics for weak interaction U in a systematic expansion and find three clearly separated time regimes: i) An initial buildup of correlations where the quasiparticles are formed. ii) An intermediate quasi-steady regime resembling a zero temperature Fermi liquid with a nonequilibrium quasiparticle distribution function. iii) The long time limit described by a quantum Boltzmann equation leading to thermalization with a temperature T proportional to U.