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

Abstract

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.

5 pages, 1 figure. To appear in Phys. Rev. Lett

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