Contour-time approach to the disordered Bose-Hubbard model in the strong coupling regime

TL;DR

This paper introduces a two-particle irreducible strong-coupling approach to analyze the disordered Bose-Hubbard model, enabling the study of both equilibrium and out-of-equilibrium phenomena, including phase diagrams and localization effects.

Contribution

It develops a novel 2PI strong-coupling formalism for the disordered BHM, allowing comprehensive analysis of equilibrium and non-equilibrium dynamics.

Findings

Identified the Mott insulator–Bose glass phase boundary.

Connected disorder strength with non-ergodic dynamics observed experimentally.

Provided equations of motion for spatio-temporal correlations in disordered BHM.

Abstract

There has been considerable interest in the disordered Bose Hubbard model (BHM) in recent years, particularly in the context of thermalization and many-body localization. We develop a two-particle irreducible (2PI) strong-coupling approach to the disordered BHM that allows us to treat both equilibrium and out-of-equilibrium situations. We obtain equations of motion for spatio-temporal correlations and explore their equilibrium solutions. We study the equilibrium phase diagram as a function of disorder strength and discuss applications of the formalism to out-of-equilibrium situations. We also note that the disorder strengths where the emergence of non-ergodic dynamics was observed in a recent experiment [Choi $et \,al.$, Science $\bf{352}$, 1547 (2016)] appear to correspond to the Mott insulator -- Bose glass phase boundary.