Strong quenches in the one-dimensional Fermi-Hubbard model

TL;DR

This paper investigates the dynamics of the one-dimensional Fermi-Hubbard model after strong interaction quenches, revealing a crossover in dominant parameters and providing an analytical approach to long-term behavior.

Contribution

It introduces an analytical method combined with iterated equations of motion to accurately describe post-quench dynamics and long-term behavior in the Fermi-Hubbard model.

Findings

Identifies a crossover from band width to local interaction dominance in dynamics.

Provides an analytical approach for infinite-time behavior without numerical averaging.

Finds no sharp dynamical transition, but a smooth crossover depending on quench strength.

Abstract

The one-dimensional Fermi-Hubbard model is used as testbed for strong global parameter quenches. With the aid of iterated equations of motion in combination with a suitable scalar product for operators we describe the dynamics and the long-term behavior in particular of the system after interaction quenches. This becomes possible because the employed approximation allows for oscillatory dynamics avoiding spurious divergences. The infinite-time behavior is captured by an analytical approach based on stationary phases; no numerical averages over long times need to be computed. We study the most relevant frequencies in the dynamics after the quench and find that the local interaction $U$ as well as the band width $W$ dominate. In contrast to former studies a crossover instead of a sharp dynamical transition depending on the strength of the quench is identified. For weak quenches the band width is more important while for strong quenches the local interaction $U$ dominates.