Correlation-induced localization Article Swipe
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· 2019
· Open Access
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· DOI: https://doi.org/10.1103/physrevb.99.104203
· OA: W2895096991
A new paradigm of Anderson localization caused by correlations in the\nlong-range hopping along with uncorrelated on-site disorder is considered which\nrequires a more precise formulation of the basic localization-delocalization\nprinciples. A new class of random Hamiltonians with translation-invariant\nhopping integrals is suggested and the localization properties of such models\nare established both in the coordinate and in the momentum spaces alongside\nwith the corresponding level statistics. Duality of translation-invariant\nmodels in the momentum and coordinate space is uncovered and exploited to find\na full localization-delocalization phase diagram for such models. The crucial\nrole of the spectral properties of hopping matrix is established and a new\nmatrix inversion trick is suggested to generate a one-parameter family of\nequivalent localization/delocalization problems. Optimization over the free\nparameter in such a transformation together with the\nlocalization/delocalization principles allows to establish exact bounds for the\nlocalized and ergodic states in long-range hopping models. When applied to the\nrandom matrix models with deterministic power-law hopping this transformation\nallows to confirm localization of states at all values of the exponent in\npower-law hopping and to prove analytically the symmetry of the exponent in the\npower-law localized wave functions.\n
