Absence of Mobility Edge in Short-range Uncorrelated Disordered Model: Coexistence of Localized and Extended States

Abstract

Unlike the well-known Mott's argument that extended and localized states should not coexist at the same energy in a generic random potential, we provide an example of a nearest-neighbor tight-binding disordered model which carries both localized and extended states without forming the mobility edge (ME). Unexpectedly, this example appears to be given by a well-studied $\beta$-ensemble with independently distributed random diagonal potential and inhomogeneous kinetic hopping terms. In order to analytically tackle the problem, we locally map the above model to the 1D Anderson model with matrix-size- and position-dependent hopping and confirm the coexistence of localized and extended states, which is shown to be robust to the perturbations of both potential and kinetic terms due to the separation of the above states in space. In addition, the mapping shows that the extended states are non-ergodic and allows to analytically estimate their fractal dimensions.

4.5 pages, 4 figures, 60 references + 3.5 pages, 5 figures in Appendices

References in corpus (19)

• Localization of interacting fermions at high temperature
• Many-body localization edge in the random-field Heisenberg chain
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Nearest neighbor tight binding models with an exact mobility edge in one dimension
• Anderson Localization of Expanding Bose-Einstein Condensates in Random Potentials
• Many-body mobility edge in a mean-field quantum spin glass
• Fractality of wave functions on a Cayley tree: Difference between a tree and a locally tree-like graph without boundary
• Self-dual quasiperiodic systems with power-law hopping
• Dynamical phases in a "multifractal" Rosenzweig-Porter model
• On the localization transition in symmetric random matrices
• Robustness of delocalization to the inclusion of soft constraints in long-range random models
• Drive Induced Delocalization in Aubry-André Model
• Quantum phase with coexisting localized, extended, and critical zones
• Emergent fractal phase in energy stratified random models
• Non-ergodic delocalized phase with Poisson level statistics
• High values of disorder-generated multifractals and logarithmically correlated processes
• Random Cantor sets and mini-bands in local spectrum of quantum systems
• Chaos due to symmetry-breaking in deformed Poisson ensemble
• Transport in deformed centrosymmetric networks

Cited by in corpus (17)

• Krylov fractality and complexity in generic random matrix ensembles
• Probing multi-mobility edges in quasiperiodic mosaic lattices
• Proposal for many-body quantum chaos detection
• Multifractal phase in the weighted adjacency matrices of random Erdös-Rényi graphs
• Robust non-ergodicity of ground state in the $\beta$ ensemble
• Reducing dynamical fluctuations and enforcing self-averaging by opening many-body quantum systems
• Long-range spectral statistics of the Rosenzweig-Porter model
• Emergent multifractality in power-law decaying eigenstates
• Re-entrant localization induced by short-range hopping in the fractal Rosenzweig-Porter Model
• Spectral form factor and energy correlations in banded random matrices
• Superdiffusion in random two dimensional system with time-reversal symmetry and long-range hopping
• Soft modes in vector spin glass models on sparse random graphs
• Power-law banded random matrix ensemble as a model for quantum many-body Hamiltonians
• Anomalous energy correlations and spectral form factor in the nonergodic phase of the $\beta$-ensemble
• Ergodicity-breaking phase diagram and fractal dimensions in long-range models with generically correlated disorder
• Quasiperiodic Skin Criticality in an Exactly Solvable Non-Hermitian Quasicrystal
• Identifying mobility edge from finite temperature spectral form factor