Abstract

Many-body localization (MBL) is the disorder-driven perfect insulating behavior of a generic interacting lattice system of local charge or spin degrees of freedom. This state of matter is an insulator at finite energy densities, fails to thermalize and violates the eigenstate thermalization hypothesis, and many-body eigenstates exhibit an area law instead of a volume law typical for thermal states. The MBL phase is separated from an ergodic disordered phase by a localization-delocalization transition that has no signatures in thermodynamics but in dynamical properties.

We here show that the eigenstates and the spectrum of the one-particle density matrix (OPDM) can be used to characterize the interaction-driven many-body localization transition in closed fermionic systems. The natural orbitals (the eigenstates of OPDM ) are localized in the many-body localized phase and spread out when one enters the delocalized phase The natural orbitals are single-particle states and share many properties with the single-particle eigenstates of an Anderson insulator. In particular, they possess exponentially decaying tails in the MBL phase. The occupation spectrum (the set of eigenvalues of OPDM ) reveals the distinctive Fock-space structure of the many-body eigenstates, exhibiting a steplike discontinuity in the localized phase. This existence discontinuity implies a close analogy between the MBL phase and a zero-temperature Fermi liquid: Both systems possess long-lived quasi-particles, are integrable and thus do not thermalize and many-body eigenstates are only weakly spread out in Fock space. We frame our results into the existing theory of the MBL phase and in particular make a connection to the emergent quasi-local conserved charges that exist in the MBL phase