Absence of mobility edge in short-range uncorrelated disordered model: Coexistence of localized and extended states!
In 1967, Sir Nevill F. Mott's pioneering work argued that the extended and the localized eigenstates in a 3-dimensional Anderson model are always separated by a critical energy called the mobility edge. The conventional wisdom has been that this energetic separation is true in any disordered low-dimensional system.
Our work shows that this is not always true in 1-dimensional systems. We identify the necessary criteria for realizing coexistent localized and extended states without forming any mobility edge: residual level repulsion, non-ergodicity of most bulk states, and spatial separation of localization centers. We demonstrate these ideas in a 1D disordered lattice governed by the Hamiltonians from the β-ensemble. We also explain the origin of the anomalous long-range correlations in the energy spectrum of the β-ensemble, which has been a long-standing puzzle in the random matrix theory community.
"Absence of mobility edge in short-range uncorrelated disordered model: Coexistence of localized and extended states"
Adway Kumar Das, Anandamohan Ghosh, Ivan M. Khaymovich Published online 18 October 2023, appeared in 20 October 2023 issue: Physical Review Letters (Vol. 131, No. 16):URL: https://link.aps.org/doi/10.1103/PhysRevLett.131.166401 DOI: 10.1103/PhysRevLett.131.166401
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Posted on: November 21st, 2023