Communications in Mathematical Physics

, Volume 332, Issue 3, pp 1017–1082 | Cite as

Asymptotic Quantum Many-Body Localization from Thermal Disorder

  • Wojciech De RoeckEmail author
  • François Huveneers


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 mn is sufficiently large.


Hubbard Model Cluster Expansion Adjacency Relation Disorder Strength Quantum Spin System 
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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Instituut voor Theoretische Fysica, K.U. LeuvenLeuvenBelgium
  2. 2.CEREMADEUniversité Paris-DauphineParis Cedex 16France

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