{"paper":{"title":"Eigenpairs of Toeplitz and disordered Toeplitz matrices with a Fisher-Hartwig symbol","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.MP","math.SP","quant-ph"],"primary_cat":"math-ph","authors_text":"Leo P. Kadanoff, Ramis Movassagh","submitted_at":"2016-04-28T03:01:36Z","abstract_excerpt":"Toeplitz matrices have entries that are constant along diagonals. They model directed transport, are at the heart of correlation function calculations of the two-dimensional Ising model, and have applications in quantum information science. We derive their eigenvalues and eigenvectors when the symbol is singular Fisher-Hartwig. We then add diagonal disorder and study the resulting eigenpairs. We find that there is a \"bulk\" behavior that is well captured by second order perturbation theory of non-Hermitian matrices. The non-perturbative behavior is classified into two classes: Runaways type I l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.08295","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}