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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 $κ(β)$, defined as the time-integrated current autocorrelation function, decays faster than any polynomial in the inverse temperature $β$ as $β\to 0$. More precisely, we define approximations $κ_τ(β)$ to $κ(β)$ by integrating the current-current autocorrelation function up to a large but finite time $τ$ and we rigorously show that $β^{-n}κ_{β^{-m}}(β)$ vanishes as $β\to 0$, for any $n,m \in \mathbb{N}$ such that $m-n$ is sufficiently large.