{"paper":{"title":"Sharp Bounds on Ground State Energy of the SYK Model","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"quant-ph","authors_text":"Arpon Basu, Pravesh K. Kothari, Siddhant Midha","submitted_at":"2026-07-29T17:54:18Z","abstract_excerpt":"We study the Sachdev-Ye-Kitaev (SYK) Hamiltonian $H_{\\operatorname{SYK}}$ on $n$ Majorana modes with $k$-body interactions, and prove that $\\mathbb{E}\\|H_{\\operatorname{SYK}}\\|_{\\operatorname{op}} = (1 - o(1))\\cdot\\sqrt{2n}/k$ for super-constant $k\\leq o(\\sqrt{n})$, where the expectation is over the disorder variables in the Hamiltonian. This confirms the predictions due to Garcia-Garcia, Jia and Verbaarschot'18 and answers a question posed in Feng, Tian and Wei'19. Our results extend to the sparse SYK Hamiltonian. As a corollary, we obtain that the dissipative quantum algorithm of Basso, Chen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.27185","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/2607.27185/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"}