Slow semiclassical dynamics of a two-dimensional Hubbard model in disorder-free potentials

TL;DR

This paper investigates the slow semiclassical dynamics of a two-dimensional Hubbard model in disorder-free potentials using the fermionic truncated Wigner approximation, revealing subdiffusive behavior and phase separation relevant for ultracold atom experiments.

Contribution

It demonstrates the validity of fTWA for longer times in 2D Hubbard models with harmonic and spin-dependent potentials, connecting to Stark many-body localization phenomena.

Findings

fTWA accurately captures dynamics for longer times with harmonic and spin-dependent potentials

Subdiffusive dynamics observed at intermediate linear potential strengths

Phase separation of ergodic and non-ergodic regions in real space

Abstract

The quench dynamics of the Hubbard model in tilted and harmonic potentials is discussed within the semiclassical picture. Applying the fermionic truncated Wigner approximation (fTWA), the dynamics of imbalances for charge and spin degrees of freedom is analyzed and its time evolution is compared with the exact simulations in one-dimensional lattice. Quench from charge or spin density wave is considered. We show that introduction of harmonic and spin-dependent linear potentials sufficiently validates fTWA for longer times. Such an improvement of fTWA is also obtained for the higher order correlations in terms of quantum Fisher information for charge and spin channels. This allows us to discuss the dynamics of larger system sizes and connect our discussion to the recently introduced Stark many-body localization. In particular, we focus on a finite two-dimensional system and show that at intermediate linear potential strength, the addition of a harmonic potential and spin dependence of the tilt, results in subdiffusive dynamics, similar to that of disordered systems. Moreover, for specific values of harmonic potential, we observed phase separation of ergodic and non-ergodic regions in real space. The latter fact is especially important for ultracold atom experiments in which harmonic confinement can be easily imposed, causing a significant change in relaxation times for different lattice locations.