{"paper":{"title":"Analytical Spectral Density of the Sachdev-Ye-Kitaev Model at finite N","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.str-el","nucl-th"],"primary_cat":"hep-th","authors_text":"Antonio M. Garc\\'ia-Garc\\'ia, Jacobus J. M. Verbaarschot","submitted_at":"2017-01-23T19:14:47Z","abstract_excerpt":"We show analytically that the spectral density of the $q$-body Sachdeev-Ye-Kitaev (SYK) model agrees with that of Q-Hermite polynomials with Q a non-trivial function of $q \\ge 2$ and the number of Majorana fermions $N \\gg 1$. Numerical results, obtained by exact diagonalization, are in excellent agreement with the analytical spectral density even for relatively small $N \\sim 8$. For $N \\gg 1$ and not close to the edge of the spectrum, we find the macroscopic spectral density simplifies to $\\rho(E) \\sim \\exp[2\\arcsin^2(E/E_0)/\\log \\eta]$, where $\\eta$ is the suppression factor of the contributi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06593","kind":"arxiv","version":3},"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"}