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Diagonalization and Many-Body Localization for a Disordered Quantum Spin Chain

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arxiv 1605.03003 v1 pith:DOGRJ6ND submitted 2016-05-10 math-ph cond-mat.dis-nnmath.MPmath.SP

John Z Imbrie This is my paper · ORCID
classification math-phcond-mat.dis-nnmath.MPmath.SP
keywords many-bodychainlocallocalizationquantumspinassumptionattraction
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We consider a weakly interacting quantum spin chain with random local interactions. We prove that many-body localization follows from a physically reasonable assumption that limits the extent of level attraction in the statistics of eigenvalues. In a KAM-style construction, a sequence of local unitary transformations is used to diagonalize the Hamiltonian by deforming the initial tensor product basis into a complete set of exact many-body eigenfunctions.

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  1. How Random Are Ergodic Eigenstates of the Ultrametric Random Matrices and the Quantum Sun Model?

    quant-ph 2025-01 conditional novelty 5.0 of 10

    Extreme value statistics of Schmidt eigenvalues reveal deviations from Wishart behavior in ergodic eigenstates of ultrametric random matrices and the Quantum Sun model.

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