Asymptotic quantum many-body localization from thermal disorder

Wojciech De Roeck; François Huveneers

doi:10.1007/s00220-014-2116-8

paper

Asymptotic quantum many-body localization from thermal disorder

arXiv:1308.6263 · doi:10.1007/s00220-014-2116-8

Abstract

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 $n, m \in N$ such that $m - n$ is sufficiently large.

53 pages, v1-->v2, revised version accepted in Comm.Math.Phys. We added an extensive outline of proofs, a glossary of symbols and more explanations in Section 5

Asymptotic quantum many-body localization from thermal disorder

Abstract

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