Many-body mobility edges in a one-dimensional model of interacting fermions

TL;DR

This paper investigates many-body localization in a one-dimensional interacting fermion system with a deterministic aperiodic potential, revealing the persistence of MBL even with single particle mobility edges and identifying transitions in entanglement and thermalization properties.

Contribution

It demonstrates that many-body localization can occur in systems with single particle mobility edges and characterizes the transition between localized and delocalized many-body states.

Findings

MBL persists with single particle mobility edges.

Transition from MBL to delocalized states at certain energies.

Eigenstate thermalization hypothesis is violated in low-energy states.

Abstract

We analyze many body localization (MBL) in an interacting one-dimensional system with a deterministic aperiodic potential. Below the threshold value of the potential $h < h_c$, the non-interacting system has single particle mobility edges at $\pm E_c$ while for $ h > h_c$ all the single particle states are localized. We demonstrate that even in the presence of single particle mobility edges, the interacting system can have MBL. Our numerical calculation of participation ratio in the Fock space and Shannon entropy shows that both for $h < h_c$ (quarter filled) and $h>h_c$ ($h\sim h_c$ and half filled), many body states in the middle of the spectrum are delocalized while the low energy states with $E < E_1$ and the high energy states with $E> E_2$ are localized. Variance of entanglement entropy (EE) also shows divergence at $E_{1,2}$ indicating a transition from MBL to delocalized regime. We also studied eigenstate thermalisation hypothesis (ETH) and found that the low energy many body states, which show area law scaling for EE do not obey ETH. The crossings from volume to area law scaling for EE and from thermal to non-thermal behaviour occurs deep inside the localised regime. For $h \gg h_c$, all the many body states remain localized for weak to intermediate strength of interaction and the system shows infinite temperature MBL phase.