Mobility edge of Stark many-body localization

TL;DR

This paper explores how a tilted potential induces energy-dependent transitions from ergodic to Stark many-body localized states in a disordered 1D fermionic system, revealing mobility edges and area-law entanglement.

Contribution

It demonstrates the existence of mobility edges in Stark many-body localization driven by a tilted potential, with finite-size scaling confirming the transition.

Findings

Mobility edges appear between delocalized and localized states.

Entanglement entropy follows area-law scaling in Stark MBL.

Transitions are diagnosed via energy-level statistics.

Abstract

We investigate many-body localization of interacting spinless fermions in a one-dimensional disordered and tilted lattice. The fermions undergo energy-dependent transitions from ergodic to Stark many-body localization driven by the tilted potential, which are manifested by the appearance of mobility edges between delocalized states and Stark many-body localized states even when the disorder is weak. We can concretely diagnose these transitions rather than crossovers by finite-size scaling of energy-level statistics. Moreover, in the Stark many-body localization, the entanglement entropy obeys the area law scaling, in analogy to that in the conventional many-body localization.