Many-body localization characterized from a one-particle perspective

TL;DR

This paper demonstrates that the one-particle density matrix effectively characterizes the many-body localization transition in fermionic systems by analyzing natural orbitals, occupation spectrum, and related entropy measures.

Contribution

It introduces a one-particle perspective to identify and analyze the many-body localization transition, revealing new indicators like the occupation spectrum and entropy.

Findings

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

The occupation spectrum shows a step-like discontinuity in the localized phase.

The occupation entropy diverges at the transition, indicating critical behavior.

Abstract

We show that the one-particle density matrix $\rho$ can be used to characterize the interaction-driven many-body localization transition in closed fermionic systems. The natural orbitals (the eigenstates of $\rho$) are localized in the many-body localized phase and spread out when one enters the delocalized phase, while the occupation spectrum (the set of eigenvalues of $\rho$) reveals the distinctive Fock-space structure of the many-body eigenstates, exhibiting a step-like discontinuity in the localized phase. The associated one-particle occupation entropy is small in the localized phase and large in the delocalized phase, with diverging fluctuations at the transition. We analyze the inverse participation ratio of the natural orbitals and find that it is independent of system size in the localized phase.