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 \({\beta \to 0}\). More precisely, we define approximations \({\kappa_{\tau}(\beta)}\) to κ(β) by integrating the current-current autocorrelation function up to a large but finite time \({\tau}\) and we rigorously show that \({\beta^{-n}\kappa_{\beta^{-m}}(\beta)}\) vanishes as \({\beta \to 0}\), for any \({n,m \in \mathbb{N}}\) such that m−n is sufficiently large.
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De Roeck, W., Huveneers, F. Asymptotic Quantum Many-Body Localization from Thermal Disorder. Commun. Math. Phys. 332, 1017–1082 (2014). https://doi.org/10.1007/s00220-014-2116-8
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DOI: https://doi.org/10.1007/s00220-014-2116-8