{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"f0189594ad187223e495c54b022eba52eb0f6d1302542d2818495a7a2c1903b7","created":"2026-10-03T07:17:53Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"0bc773e5c7c967ac2182b8b763ede14c2e63336cc09ed24099a137a5acb71363","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":"1","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 $s_{\\mathrm{exp}}$ 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 $s_{\\mathrm{exp}} - s*$. Answer: $s*$ with error bars from controlled finite-temperature numerics and the ratio $s_{\\mathrm{exp}}/s*$.","problem_ref":null,"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 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