Many-body localization and mobility edge in a disordered Heisenberg spin ladder

TL;DR

This paper investigates how disorder and interactions cause many-body localization in a Heisenberg spin ladder, revealing a phase transition, a mobility edge, and the growth of a mobility gap with increasing disorder.

Contribution

It demonstrates the existence of a mobility edge in a disordered Heisenberg ladder and characterizes the quantum phase transition to full many-body localization.

Findings

Identified a critical disorder strength $h_c \,\sim\, 8.5$ for localization transition.

Discovered a mobility edge separating localized and delocalized energy states.

Showed the mobility gap increases with disorder, leading to full localization.

Abstract

We examine the interplay of interaction and disorder for a Heisenberg spin ladder system with random fields. We identify many-body localized states based on the entanglement entropy scaling, where delocalized and localized states have volume and area laws, respectively. We first establish the quantum phase transition at a critical random field strength $h_c \sim 8.5\pm 0.5$, where all energy eigenstates are localized beyond that value. Interestingly, the entanglement entropy and fluctuation of the bipartite magnetization show distinct probability distributions which characterize different quantum phases. Furthermore, we show that for weaker $h$, energy eigenstates with higher energy density are delocalized while states at lower energy density are localized. This defines a mobility edge and a mobility gap separating these two phases. By following the evolution of low energy eigenstates, we observe that the mobility gap grows with increasing the random field strength, which drives the system to the phase of the full many-body localization with increasing disorder strength.