{"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 sample","topic_ref":null},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"26988ac51040766818826a94ce04dab7276886d45bdf6202edee12b9012fd5de","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"dba119644e687b9a112de230333958b7d55e134489d3cfa3ddc5d4e57e40b7fb","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"Qn848bnIVeS469qvMPXnWKuegqYrqMNnwRsqF5BP4Gs7AT4grNi-nWp2hEggjEvH3Cj_eUdUvTh-9lcfnVjgDA"},"schema":"pubphys.envelope/1"},"record_hash":"26988ac51040766818826a94ce04dab7276886d45bdf6202edee12b9012fd5de","leaf_index":2232}