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

Understand

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.