Three-dimensional dynamics of a fermionic Mott wedding-cake in clean and disordered optical lattices

TL;DR

This study investigates the real-time expansion dynamics of a fermionic Mott insulator in three dimensions, revealing multiple timescales in melting, effects of disorder, and the interplay between localization and Mott stability.

Contribution

It introduces a combined time-dependent density-functional and dynamical mean-field theory approach to analyze high-dimensional, disordered, strongly correlated fermionic systems.

Findings

Mott plateau persists longer than band insulator during expansion

Disorder destabilizes the Mott plateau and can reduce localization

Multiple timescales observed in the melting process

Abstract

Non-equilibrium quantum phenomena are ubiquitous in nature. Yet, theoretical predictions on the real-time dynamics of many-body quantum systems remain formidably challenging, especially for high dimensions, strong interactions or disordered samples. Here we consider a notable paradigm of strongly correlated Fermi systems, the Mott phase of the Hubbard model, in a setup resembling ultracold-gases experiments. We study the three-dimensional expansion of a cloud into an optical lattice after removing the confining potential. We use time-dependent density-functional theory combined with dynamical mean-field theory, considering interactions below and above the Mott threshold, as well as disorder effects. At strong coupling, we observe multiple timescales in the melting of the Mott wedding-cake structure, as the Mott plateau persist orders of magnitude longer than the band insulating core. We also show that disorder destabilises the Mott plateau and that, compared to a clean setup, localisation can decrease, creating an interesting dynamic crossover during the expansion.