Localization Dynamics from Static and Mobile Impurities

TL;DR

This paper investigates how static and mobile impurities affect superfluidity and localization in a bosonic ladder model, revealing different localization behaviors and a many-body localized phase through analytical and numerical methods.

Contribution

It introduces a detailed analysis of impurity-induced localization and superfluid response, including a local $ ext{Z}_2$ gauge theory and effective quantum spin models, expanding understanding of impurity effects in quantum ladders.

Findings

Weakly-coupled rungs exhibit power-law localization.

Strongly-coupled rungs lead to steep localization or insulating phases.

Many-body localization observed after a quench in disordered systems.

Abstract

We study the superfluid response and localization dynamics from static and mobile impurities. The superfluidity is formed in the rung-Mott phase of a bosonic ladder model producing spin-Meissner currents induced by a $\mathbb{U}(1)$ gauge field or a uniform magnetic field. Impurities are described through two-state systems which act as a two-peak random potential. An impurity sits either at the top or at the bottom of the ladder on each rung equally, producing a telegraph signal. The impurities-matter coupling gives rise to a classical Ising symmetry for static and mobile impurities associated to the inversion symmetry of the two legs of the ladder. From the decoupled rungs limit, we also identify a local $\mathbb{Z}_2$ gauge theory for mobile impurities. The properties of the system are studied from an effective quantum spin model including the possibility of four-body coupling in the limit of a strong interaction between bosons and impurities. Through analytical approaches and numerical exact diagonalization, we study the superfluid currents both in the weakly-coupled and strongly-coupled rungs limits for the bosons. In the weakly-coupled rungs situation, we find a smooth power-law localization whereas the strongly-coupled rungs limit produces a steep localization or insulating phase for various configurations of the two-peak random potential. In the strongly disordered situation, through entanglement and bipartite fluctuation measures, we also identify a many-body localization regime in time after a quench of the system when prepared in a N\' eel state.