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

TL;DR

This study investigates many-body localization in a disordered 1D Bose-Hubbard model by analyzing single-particle properties, revealing how natural orbitals and density distributions signal the ergodic-MBL transition, with implications for experimental detection.

Contribution

It introduces a novel single-particle perspective to characterize Fock-space localization in the Bose-Hubbard model, linking natural orbitals and density distributions to the MBL transition.

Findings

Natural orbitals are extended in the ergodic phase and localized in the MBL phase.

Distributions of natural orbital occupations serve as measures of Fock-space localization.

Density distributions provide a one-particle observable for detecting the ergodic-MBL transition.

Abstract

We numerically investigate 1D Bose-Hubbard chains with onsite disorder by means of exact diagonalization. A primary focus of our work is on characterizing Fock-space localization in this model from the single-particle perspective. For this purpose, we compute the one-particle density matrix (OPDM) in many-body eigenstates. We show that the natural orbitals (the eigenstates of the OPDM) are extended in the ergodic phase and real-space localized when one enters into the MBL phase. Furthermore, the distributions of occupations of the natural orbitals can be used as measures of Fock-space localization in the respective basis. Consistent with previous studies, we observe signatures of a transition from the ergodic to the many-body localized (MBL) regime when increasing the disorder strength. We further demonstrate that Fock-space localization, albeit weaker, is also evidently present in the distribution of the physical densities in the MBL regime, both for soft- and hardcore bosons. 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.