{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"be26a5479bd2bbcddf6655fba72b4c03f0f43eee9d9aaa5192e19b87f218c05f","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b","f1754c92b010a70d32976ca358aff734bf0391f3b1de380b48340927eda5a08a"],"salt":"1f2444027f74aad4a9f3dc1df74592610273bb442ab889da716c3179cc5f84fb","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"amo.hubbard-simulation.doped-entropy-floor","kind":"well-posed","literature_status":"open","n":"2","parents":[],"plain":"Pairing in the Hubbard model needs very cold atoms, and the best experiments reached their coldest temperatures only at half filling, one atom per site. The question is how cold a doped sample with holes can be made, and what stops further cooling.","posed_since":"","precise":"Homogeneous (flat-bottom) 2D square-lattice Fermi-Hubbard sample with at least 100 sites, $U/t = 8$, hole doping $\\delta = 0.1\\ \\text{to}\\ 0.2$. Determine the minimum entropy per site $s_{\\min}$ (units of $k_{B}$) and temperature $T/t$ reachable by entropy redistribution into reservoirs and adiabatic loading, with independent thermometry, and identify the limiting heating processes (lattice-light scattering, technical noise, reservoir capacity). Answer: $s_{\\min}$ and $T/t$ in the doped region with an error budget, and whether $T/t < 0.05$ is reachable at $\\delta = 0.125$.","problem_ref":"f1754c92b010a70d32976ca358aff734bf0391f3b1de380b48340927eda5a08a","references":"","settled_by":"A doped homogeneous sample with thermometry validated against finite-temperature numerics, plus a measured heating budget.","status_note":"A 2025 experiment reached $T/t = 0.05 (+0.06/-0.05)$ at half filling by entropy redistribution (Xu et al., Nature 642, 909, arXiv:2502.00095).","title":"Lowest entropy per site reachable in a doped homogeneous Hubbard 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