{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"a24089be51dff802c643623acc091bb60387867dde76ccb29216432ef7b5a139","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b","d688eea65cb382d1f773baba20d2c71c378fc0aa5993687266cf705c35eb87ec"],"salt":"9756a781c0add4d0d5d24eddf1effaac5eaed5cf06468ea7f71c7ad15ee5fbaf","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"amo.hubbard-simulation.entropy-threshold","kind":"well-posed","literature_status":"open","n":"2","parents":[],"plain":"Cooling atoms in a lattice is limited by how much disorder (entropy) remains per site. The question is how far below today's best entropy an experiment must go before pairing becomes visible.","posed_since":"","precise":"Let $s_{\\exp}$ be the entropy per site (units of $k_B$) reached in current doped quantum-gas-microscope samples. For the 2D Hubbard model at $U/t = 8$, $\\delta = 0.125$, $t'/t = -0.2$, determine the entropy per site $s*$ below which the d-wave pair correlation length exceeds 10 lattice sites, and hence the required reduction $s_{\\exp} - s*$. Answer: $s*$ with error bars from controlled finite-temperature numerics and the ratio $s_{\\exp}/s*$.","problem_ref":"d688eea65cb382d1f773baba20d2c71c378fc0aa5993687266cf705c35eb87ec","references":"","settled_by":"Controlled finite-temperature numerics (for example diagrammatic Monte Carlo or tensor-network methods with error bars) giving the pair correlation length as a function of entropy per site at the stated parameters.","status_note":"Ground-state DMRG and auxiliary-field quantum Monte Carlo find d-wave order coexisting with partially filled stripes at $t' \\ne 0$ (Xu et al., Science 2024); controlled finite-temperature values of $s*$ are lacking.","title":"Entropy reduction needed to see d-wave correlations in Hubbard simulators","topic_ref":null},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"257bdb30d6db8f86e08caea40cec4ce16d570b4d9c8a97d91bb6726cb02585f9","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"389530f7a67dd35e20e4b5d2a5623668a0eb72c9f527b0df5891b53508adf179","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"1iWpPLz-8M8sh2T53EisK8ELzoT2MkXUQJGz4sx-ALGFkJrYehDgxgpVky4pypynoH8p2svbR5iFUtC5ItltBg"},"schema":"pubphys.envelope/1"},"record_hash":"257bdb30d6db8f86e08caea40cec4ce16d570b4d9c8a97d91bb6726cb02585f9","leaf_index":2234}