{"paper":{"title":"Transition from localized to extended eigenstates in the ensemble of power-law random banded matrices","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat","authors_text":"Alexander D. Mirlin, Frank-Michael Dittes, Javier Quezada, Thomas H. Seligman, Yan V. Fyodorov","submitted_at":"1996-04-26T16:11:44Z","abstract_excerpt":"We study statistical properties of the ensemble of large $N\\times N$ random matrices whose entries $ H_{ij}$ decrease in a power-law fashion $H_{ij}\\sim|i-j|^{-\\alpha}$. Mapping the problem onto a nonlinear $\\sigma-$model with non-local interaction, we find a transition from localized to extended states at $\\alpha=1$. At this critical value of $\\alpha$ the system exhibits multifractality and spectral statistics intermediate between the Wigner-Dyson and Poisson one. These features are reminiscent of those typical for the mobility edge of disordered conductors. We find a continuous set of critic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/9604163","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/cond-mat/9604163/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}