Many-body localization characterized from a one-particle perspective

Understand

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.