Many-body delocalization transition and relaxation in a quantum dot

Abstract

We revisit the problem of quantum localization of many-body states in a quantum dot and the associated problem of relaxation of an excited state in a finite correlated electron system. We determine the localization threshold for the eigenstates in Fock space. We argue that the localization-delocalization transition (which manifests itself, e.g., in the statistics of many-body energy levels) becomes sharp in the limit of a large dimensionless conductance (or, equivalently, in the limit of weak interaction). We also analyze the temporal relaxation of quantum states of various types (a "hot-electron state", a "typical" many-body state, and a single-electron excitation added to a "thermal state") with energies below, at, and above the transition.

16+6 pages, 2 figures; comments, additional explanations, references, and Supplemental Material added

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• Multifractality of eigenstates in the delocalized non-ergodic phase of some random matrix models : Wigner-Weisskopf approach
• Energy transport in the Anderson insulator
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• Role of Fock-space correlations in many-body localization
• Emergence of many-body quantum chaos via spontaneous breaking of unitarity
• Dynamical thermalization in isolated quantum dots and black holes
• Many-body localization enables iterative quantum optimization
• Ergodicity-to-localization transition on random regular graphs with large connectivity and in many-body quantum dots
• Localization transition in random Levy matrices : multifractality of eigenvectors in the localized phase and at criticality
• Cyclic Quantum Annealing: Searching for Deep Low-Energy States in 5000-Qubit Spin Glass
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