Strongly interacting bosons in multi-chromatic potentials supporting mobility edges: localization, quasi-condensation and expansion dynamics

TL;DR

This paper investigates the static and dynamic behaviors of strongly interacting bosons in a one-dimensional quasiperiodic potential with mobility edges, revealing how localization and delocalization influence quasi-condensation and expansion.

Contribution

It provides exact numerical analysis of hard-core bosons in multi-chromatic potentials, linking spectral properties to many-body localization and dynamics.

Findings

System behaves as a quasi-condensate or insulator depending on the Fermi surface location.

Partial localization during expansion is determined by the single-particle spectrum.

Exact results connect spectral delocalization with many-body dynamical behavior.

Abstract

We provide an account of the static and dynamic properties of hard-core bosons in a one-dimensional lattice subject to a multi-chromatic quasiperiodic potential for which the single-particle spectrum has mobility edges. We use the mapping from strongly interacting bosons to weakly interacting fermions, and provide exact numerical results for hard-core bosons in and out of equilibrium. In equilibrium, we find that the system behaves like a quasi-condensate (insulator) depending on whether the Fermi surface of the corresponding fermionic system lies in a spectral region where the single-particle states are delocalized (localized). We also study non-equilibrium expansion dynamics of initially trapped bosons, and demonstrate that the extent of partial localization is determined by the single-particle spectrum.