2025/11/23 by Pouranvari, Mohammad
Physics and Astronomy · #FOS: Physical sciences #Quantum and electron transport phenomena #Quantum many-body systems #Strongly Correlated Electrons (cond-mat.str-el) #Topological Materials and Phenomena
paper · doi:10.48550/arxiv.2511.18341
openalex publication_date 2025/11/23 · openalex created_date 2025/11/27 · openalex updated_date 2026/07/28
We investigate a one-dimensional tight-binding model in which onsite potentials \εi\ exhibit power-law spatialcorrelations (with exponent α) and the hopping amplitudes decay as tij∼ |i-j|-β. This two-parameter family interpolates continuously between short-range Anderson-like disorder, correlated disorder with conventional hopping, and long-range hopping models with nontrivial delocalization tendencies. Using large-scale exact diagonalization, we construct a comprehensive phase map in the (α,β) plane by combining spectral statistics, density-of-states analysis, and energy-resolved localization indicators such as the participation ratio, single-particle entanglement entropy, level-spacing ratio r, and the ratio of the geometric to arithmetic density of states. From these observables we define phase-indicator functions that compactly quantify localization behavior across the spectrum. Our analysis reveals robust mobility edges and multiple regimes of spectral coexistence between localized, extended, resonant, and critical states. Finite-size scaling, implemented via an explicit smoothness-based cost function, enables extraction of critical exponents and delineation of transition lines across the (α,β) parameter space. To validate and complement these physics-based diagnostics, we employ a supervised autoencoder that learns high-level representations of eigenstate structure directly from raw features and reliably reproduces the phase classification defined by the indicator functions. Together, these approaches provide a coherent and internally consistent picture of the spectral transitions driven by correlated disorder and long-range hopping, establishing a unified framework for characterizing mobility edges in long-range one-dimensional systems.