Many-body localization in system with a completely delocalized single-particle spectrum

Abstract

Many-body localization (MBL) in a one-dimensional Fermi Hubbard model with random on-site interactions is studied. While for this model all single-particle states are trivially delocalized, it is shown that for sufficiently strong disordered interactions the model is many-body localized. It is therefore argued that MBL does not necessary rely on localization of the single-particle spectrum. This model provides a convenient platform to study pure MBL phenomenology, since Anderson localization in this model does not exist. By examining various forms of the interaction term a dramatic effect of symmetries on charge transport is demonstrated. A possible realization in a cold atom experiments is proposed. Introduction.-It has been known for almost 60 years that non-interacting particles in one-dimensional disordered systems exhibit Anderson localization [1]. Transport in these systems is exponentially suppressed with the system size, and without coupling to the environment, these systems are non-ergodic at any temperature. Anderson localized systems are, however, non-generic, since they do not include interactions which allow for the exchange of energy. For many years it was assumed that interactions generally restore ergodicity and destroy localization [2]. A decade ago, using non-equilibrium diagrammatic techniques, it was argued that Anderson localization is stable under the addition of a small shortranged interactions [3], a phenomenon currently known as many-body localization (MBL). Many-body localized systems are the only known generic non-ergodic systems which do not follow the assumptions of statistical mechanics [4][5][6]. While the realization of MBL systems presents challenges in condensed matter systems due to inevitable presence of phonons [7,8], recent experiments in cold atoms have provided evidence of the existence of MBL in both one-dimensional [9-11] and two-dimensional systems [12].

Many-Body Localization for Randomly Interacting Bosons

“…Such a system reveals MBL while, when the interactions are turned off, the randomness disappears and the system has extended, single particle eigenstates. In later works, a similar phenomenon was observed for fermions [17,18]. We shall consider the bosonic system in more detail here providing an understanding of the observed MBL via a perturbative model, extending and clarifying the results reported in [16].…”

“…Going further into the delocalized regime (smaller U in our case) β = 1 but γ decreases to 0 reaching a GOE Gaussian tail in the fully ergodic regime. In the transition region, for U ∈ [10,17], slightly better fits are obtained fitting simultaneously β and γ. Bearing in mind that (6) is necessarily an approximate fitting formula -reducing e.g.…”

Dynamics of strongly interacting systems: From Fock-space fragmentation to many-body localization

“…V t, W . As a first approximation, we consider the limit V /t → ∞ [55][56][57][58][59] . In this regime the spectrum ofĤ splits into energetically separated bands composed by states with identical number of pairs of nearest-neighbor occupied sites N •• ≡ xn xnx+1 , which we name bonds 55 .…”

Algebraic many-body localization and its implications on information propagation

“…The existence of the MBL-phase has been confirmed in several numerical works 10,[29][30][31][32][33][34][35] as well as experimentally using quantum simulators, such as ultracold atoms in optical lattices [36][37][38][39] and trapped ions 40 . Moreover, systems where the single-particle spectrum is fully (or partially) delocalized have also been found to show MBL [41][42][43][44] . Thus it is not necessary to have exponentially localized single-particle states a priori for MBL to exist.…”