{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"81dc2f2fcd889717904e451a1a16693c66d3c7ff18a73b1d93747594bf177798","created":"2026-10-03T07:18:00Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"7abc6c61b6c81207cabc87810ba5440ad99fb6121e05c864451c85783f2e1b57","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"cm.hubbard-mott.pure-model-sc","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[],"plain":"With only nearest-neighbor hopping, the most accurate computer methods find stripes of charge and spin instead of superconductivity, but competing states lie very close in energy.","posed_since":"1987","precise":"For the square-lattice Hubbard model with $t' = 0$, $U/t = 6\\ \\text{to}\\ 8$ and hole doping $\\delta = 1/8$, determine whether the ground state in the thermodynamic limit has long-range d-wave superconducting order or a stripe state whose pair correlations decay to zero. An answer is a controlled extrapolation of the pairing order parameter from at least two independent methods (DMRG, AFQMC, iPEPS, DMET) with consistent error bars.","problem_ref":null,"references":"","settled_by":"Agreement of independent unbiased methods on the extrapolated d-wave order parameter at $\\delta=1/8$ with error bars smaller than its claimed value.","status_note":"A multi-method study (2020) found filled stripes and no long-range d-wave order for $t' = 0$ at $\\delta = 1/8$; competing uniform superconducting states lie close in energy.","title":"Does the pure square-lattice Hubbard model superconduct at moderate doping","topic_ref":"c72f37399f69cded53ebd299920fa33be67ae1baf0e499d87c1962d53668d71d"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"b0460b1a4a3874a3dc74e099f83ba7351392ca53bfc3795b23a67ade788c04ea","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"471988c567915b82c1b50bd33c76f43f28923fb9a3a420317981b8ed6dae0266","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"KVn1hb2pgqFI6rP0snDRKbZ2D83AQtOCrThdF7jDYO5V2wtqJG2J-OglVVznfpuDyz308jVctKGIjeuLP82NDQ"},"schema":"pubphys.envelope/1"},"record_hash":"b0460b1a4a3874a3dc74e099f83ba7351392ca53bfc3795b23a67ade788c04ea","leaf_index":1026}