Tunable transport in the mass-imbalanced Fermi-Hubbard model

TL;DR

This paper investigates transport phenomena in a one-dimensional mass-imbalanced Fermi-Hubbard model, revealing a crossover from ballistic to diffusive behavior and validating the quantum Boltzmann approach against experimental and numerical results.

Contribution

It introduces a quantum Boltzmann framework for analyzing transport in mass-imbalanced Hubbard models, bridging theory with experimental observations.

Findings

Transport transitions from ballistic to diffusive depending on mass ratio.

Quantum Boltzmann results agree with matrix product operator simulations.

Transport slows and becomes subdiffusive under a tilt, matching experimental data.

Abstract

The late-time dynamics of quantum many-body systems is organized in distinct dynamical universality classes, characterized by their conservation laws and thus by their emergent hydrodynamic transport. Here, we study transport in the one-dimensional Hubbard model with different masses of the two fermionic species. To this end, we develop a quantum Boltzmann approach valid in the limit of weak interactions. We explore the crossover from ballistic to diffusive transport, whose timescale strongly depends on the mass ratio of the two species. For timescales accessible with matrix product operators, we find excellent agreement between these numerically exact results and the quantum Boltzmann equation, even for intermediate interactions. We investigate two scenarios which have been recently studied with ultracold atom experiments. First, in the presence of a tilt, the quantum Boltzmann equation predicts that transport is significantly slowed down and becomes subdiffusive, consistent with previous studies. Second, we study transport probed by displacing a harmonic confinement potential and find good quantitative agreement with recent experimental data [N. Darkwah Oppong et al., arXiv:2011.12411]. Our results demonstrate that the quantum Boltzmann equation is a useful tool to study complex non-equilibrium states in inhomogeneous potentials, as often probed with synthetic quantum systems.