Asymptotic Quantum Many-Body Localization from Thermal Disorder

We consider a quantum lattice system with infinite-dimensional on-site Hilbert space, very similar to the Bose-Hubbard model. We investigate many-body localization in this model, induced by thermal fluctuations rather than disorder in the Hamiltonian. We provide evidence that the Green-Kubo conductivity kappa(beta), defined as the time-integrated current autocorrelation function, decays faster than any polynomial in the inverse temperature beta as . More precisely, we define approximations to kappa(beta) by integrating the current-current autocorrelation function up to a large but finite time and we rigorously show that vanishes as , for any such that m-n is sufficiently large.