Configuration-Controlled Many-Body Localization and the Mobility Emulsion

TL;DR

This paper introduces a novel non-ergodic phase called the mobility emulsion in disordered interacting bosons, characterized by coexistence of localized and extended states, controllable by initial many-body configurations, challenging traditional views of many-body localization.

Contribution

The study uncovers a new phase, the mobility emulsion, distinguished by configuration-dependent coexistence of localized and extended states, and demonstrates its properties and potential observability in cold atom systems.

Findings

Identifies a mobility emulsion phase with coexisting localized and extended states.

Shows the phase's properties depend on initial many-body configurations.

Demonstrates the phase's potential observability in cold atom experiments.

Abstract

We uncover a new non-ergodic phase, distinct from the many-body localized (MBL) phase, in a disordered two-leg ladder of interacting hardcore bosons. The dynamics of this emergent phase, which has no single-particle analog and exists only for strong disorder and finite interaction, is determined by the many-body configuration of the initial state. Remarkably, this phase features the $\textit{coexistence}$ of localized and extended many-body states at fixed energy density and thus does not exhibit a many-body mobility edge, nor does it reduce to a model with a single-particle mobility edge in the noninteracting limit. We show that eigenstates in this phase can be described in terms of interacting emergent Ising spin degrees of freedom ("singlons") suspended in a mixture with inert charge degrees of freedom ("doublons" and "holons"), and thus dub it a $\textit{mobility emulsion}$ (ME). We argue that grouping eigenstates by their doublon/holon density reveals a transition between localized and extended states that is invisible as a function of energy density. We further demonstrate that the dynamics of the system following a quench may exhibit either thermalizing or localized behavior depending on the doublon/holon density of the initial product state. Intriguingly, the ergodicity of the ME is thus tuned by the initial state of the many-body system. These results establish a new paradigm for using many-body configurations as a tool to study and control the MBL transition. The ME phase may be observable in suitably prepared cold atom optical lattices.