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Many-body Localization of Cold

In the seminal 1958 paper, Anderson cites the problem of spin diffusion as a motivation to study the quantum effect of localization [1]. The conclusion about the stability of a localized phase was actually reached there for a single quasiparticle hopping between sites with random, broadly distributed energies. The single-particle localization theory, applicable to various systems comprised of noninteracting particles, provided a framework for understanding a broad range of physical phenomena including, e.g., the metal-insulator transition in electric conduction of solids [2]. In the latter example, the interference correction to Drude conductivity of the metallic phase serves as a harbinger of the transition to localized, insulating state. The interaction between electrons leads to temporal noise of a self-consistent potential acting on electrons. The noise results in electron phase relaxation, which in turn reduces the role of interference effects. Would the interaction destroy the effect of localization? Getting back to Ref. [1], we note that a highly-excited spin system can hardly be described in terms of non-interacting quasiparticles. Anderson made, however, an insightful remark: as long as the system is isolated from a “real external bath”, the localization effect preventing thermal equilibration within an isolated body, may withstand interactions. This view, for the case of short-range interaction, was re-affirmed in a later paper [3]. The problem of many-body localization (MBL) was revisited a decade ago by Basko, Aleiner, and Altshuler [5] who investigated the mobility edge of weakly-interacting electrons in a random potential. The MBL problem for finite-bandwidth fermions was addressed by Oganesyan and Huse [4]. The conclusion was that interaction does not destroy the localization effect in an isolated electron system: an initial local perturbation of an intensive