Many-body mobility edge in a quasi periodic system

Sabyasachi Nag, Arti Garg

Published 2017-01-01Version 1

We analyze many body localization (MBL) in an interacting quasi-periodic system in one-dimension. We explore effects of nearest-neighbour repulsion on a system of spin-less fermions in which below a threshold value of quasi-periodic potential $h < h_c$, the system has single particle mobility edge at $\pm E_c$ while for $ h > h_c$ all the single particle states are localized. We demonstrate based on our numerical calculation of participation ratio in the Fock space and Shannon entropy, that both for $h < h_c$ and $h > h_c$, the interacting system can have many-body mobility edge. For $h < h_c$, if the system is away from half-filling then the corresponding interacting system shows MBL for a set of low energy many body states ($E <E_1$) for weak to intermediate values of interaction. The states in the middle of the many body spectrum are delocalised while the very high energy states $E> E_2$ are localized. On the other hand for $h < h_c$ if the system is at half filling, the interacting system remains delocalised and does not show MBL for any strength of interaction. We also studied the energy resolved entanglement entropy and eigenstate thermalisation hypothesis (ETH) in this system and found that the low energy many body states, which show area law scaling for entanglement entropy also do not obey ETH. The crossings from volume to area law scaling for entanglement entropy and from thermal to non-thermal behaviour occurs at characteristic energies $\tilde{E_1}< E_1$ and $\tilde{E_2}>E_2$ indicating that Shannon entropy and participation ratio in Fock space overestimates the extend of localized regime.