Correlation-induced localization

Conventional Anderson localization is due to destructive interference of matter waves described by local random Hamiltonians. Correlations in random diagonal elements of such a Hamiltonian are known to favor delocalization. Systems described by nonlocal Hamiltonians have become experimentally accessible recently. The authors consider two families of such random-matrix Hamiltonians with correlations in the long-range hopping terms and demonstrate that, as correlations become stronger, localization is enhanced while the wave-function ergodicity progressively deteriorates.