Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.18341 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908670821924864 |
|---|---|
| author | Pouranvari, Mohammad |
| author_facet | Pouranvari, Mohammad |
| contents | We investigate a one-dimensional tight-binding model in which onsite
potentials $\{\varepsilon_i\}$ exhibit power-law spatial correlations
(with exponent $α$) and the hopping amplitudes decay as
$t_{ij}\sim |i-j|^{-β}$. 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 behaviour 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_18341 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Interplay of Power-Law correlated Disorder and Long-Range Hopping in One Dimension: Mobility Edges, Criticality, and ML-Based Phase Identification Pouranvari, Mohammad Strongly Correlated Electrons We investigate a one-dimensional tight-binding model in which onsite potentials $\{\varepsilon_i\}$ exhibit power-law spatial correlations (with exponent $α$) and the hopping amplitudes decay as $t_{ij}\sim |i-j|^{-β}$. 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 behaviour 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. |
| title | Interplay of Power-Law correlated Disorder and Long-Range Hopping in One Dimension: Mobility Edges, Criticality, and ML-Based Phase Identification |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2511.18341 |