Asymptotic quantum many-body localization from thermal disorder
A quantum lattice system is considered akin to the Bose-Hubbard model. The many-body localization is investigated, that is induced by thermal fluctuations rather than by the disorder in the Hamiltonian. This is an important departure from current approaches to the delocalization-localization (or metal-insulator) transition, normally expected to occur with the growth of the disorder strength. Major rigorous results about the localized regime have been obtained in the context of non-interacting electrons in random lattices. The authors address a difficult problem of how many-body interactions modify the metal-insulator transition. There is a consensus that the latter transition occurs at least for short range interactions. However, there is no mathematical proof of many-body localization. All models considered so far have a disorder built-in in the Hamiltonian. Here the perspective changes and amounts to replacing that disorder by thermal fluctuations, due to the thermal Gibbs state. A characterization of localization is given in terms of the dynamics of energy fluctuations which is embodied by the Green-Kubo formula for the heat conductivity. The many body localization is understood as the vanishing of conductivity. The main result of the paper is a demonstration that the Green-Kubo conductivity in the considered model decays faster than any polynomial if the inverse temperature \(\beta \) as \(\beta \rightarrow 0\).
eigenstate thermalization hypothesis (ETH)
scientific article; zbMATH DE number 6359803
scientific article