Many-body localization from a one-particle perspective in the disordered 1D Bose-Hubbard model

We numerically investigate 1D Bose-Hubbard chains with onsite disorder by means of exact diagonalization. Consistent with previous studies, we observe signatures of transition from the ergodic to the many-body localized (MBL) regime when increasing the disorder strength or energy density. Apart form the entanglement entropy as a conventional but indirect measure for the ergodic-MBL transition we utilise the one-particle density matrix (OPDM) to characterize the system [1]. We show that the natural orbitals (the eigenstates of OPDM) are extended in the ergodic phase and real-space localized when one enters into the MBL phase. Furthermore, the distributions of occupancies of the natural orbitals as well as the diagonal part of OPDM (i.e., the site occupancies) can be used as measures of Fock-space localization in the respective basis [2]. Moreover, the full distribution of the densities of the physical particles provides a one-particle measure for the detection of the ergodic-MBL transition which could be directly accessed in experiments with ultra-cold gases.

[1] S. Bera, H. Schomerus, F. Heidrich-Meisner and J.H. Bardarson, PRL 115, 046603 (2015).
[2] M. Hopjan and F. Heidrich-Meisner, in preparation.