Eur. Phys. J. B (2016) 89: 77
https://doi.org/10.1140/epjb/e2016-60873-4

Regular Article

Many-body ground state localization and coexistence of localized and extended states in an interacting quasiperiodic system

¹ Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, P.R. China
² Collaborative Innovation Center of Quantum Matter, Beijing, P.R. China

^a e-mail: nawyucheng@163.com

Received: 5 November 2015
Received in final form: 18 January 2016
Published online: 23 March 2016

Abstract

We study the localization problem of one-dimensional interacting spinless fermions in an incommensurate optical lattice, which changes from an extended phase to a non-ergoic many-body localized phase by increasing the strength of the incommensurate potential. We identify that there exists an intermediate regime before the system enters the many-body localized phase, in which both the localized and extended many-body states coexist, thus the system is divided into three different phases, which can be characterized by normalized participation ratios of the many-body eigenstates and distributions of natural orbitals of the corresponding one-particle density matrix. This is very different from its noninteracting limit, in which all eigenstates undergo a delocalization-localization transition when the strength of the incommensurate potential exceeds a critical value.