Asymptotic Quantum Many-Body Localization from Thermal Disorder

© 2014, Springer-Verlag Berlin Heidelberg. 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→0. More precisely, we define approximations κτ(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-nκβ-m(β) vanishes as β→0, for any n, m∈ 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 5status: publishe