{"paper":{"title":"Dynamical scaling near the pseudogap quantum critical point of the two-dimensional Hubbard model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The two-dimensional Hubbard model shows ω/T scaling of the form tanh(ω/2T) in spin and current susceptibilities near its pseudogap quantum critical point.","cross_cats":[],"primary_cat":"cond-mat.str-el","authors_text":"Andreas Gleis, Gabriel Kotliar, Jan von Delft, Mathias Pelz","submitted_at":"2026-05-14T16:50:40Z","abstract_excerpt":"We study dynamical scaling in the quantum-critical fan of the pseudogap-metal to Fermi-liquid transition of the two-dimensional Hubbard model. Using a four-patch dynamical cluster approximation with the numerical renormalization group as a cluster impurity solver, we access real-frequency dynamics over several decades at arbitrary temperatures. Close to the critical doping, the local spin and cluster-current susceptibility spectra exhibit $x=\\omega/T$ scaling of the form $\\chi''(\\omega,T)\\sim \\tanh(x/2)$, and the cluster contribution to the optical conductivity obeys $T\\sigma'_{\\mathrm{cl}}(\\o"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Close to the critical doping, the local spin and cluster-current susceptibility spectra exhibit x=ω/T scaling of the form χ''(ω,T)∼tanh(x/2), and the cluster contribution to the optical conductivity obeys Tσ'cl(ω,T)∼tanh(x/2)/x, implying a 1/T cluster dc conductivity.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the four-patch DCA with NRG solver faithfully captures the low-energy dynamics and vertex corrections near the pseudogap QCP without significant finite-size or approximation artifacts that would alter the reported scaling forms.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Numerical evidence shows ω/T scaling in susceptibilities and 1/T cluster conductivity near the pseudogap QCP in the 2D Hubbard model, consistent with marginal-Fermi-liquid self-energy and strange-metal transport.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The two-dimensional Hubbard model shows ω/T scaling of the form tanh(ω/2T) in spin and current susceptibilities near its pseudogap quantum critical point.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"5646ab8227be6ad28a632922ab2302ced9027f9524d4a28da88429ebd5c25fb5"},"source":{"id":"2605.15060","kind":"arxiv","version":1},"verdict":{"id":"ad4b7eba-e264-45bd-8d38-874e61ebd970","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T14:05:37.435641Z","strongest_claim":"Close to the critical doping, the local spin and cluster-current susceptibility spectra exhibit x=ω/T scaling of the form χ''(ω,T)∼tanh(x/2), and the cluster contribution to the optical conductivity obeys Tσ'cl(ω,T)∼tanh(x/2)/x, implying a 1/T cluster dc conductivity.","one_line_summary":"Numerical evidence shows ω/T scaling in susceptibilities and 1/T cluster conductivity near the pseudogap QCP in the 2D Hubbard model, consistent with marginal-Fermi-liquid self-energy and strange-metal transport.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the four-patch DCA with NRG solver faithfully captures the low-energy dynamics and vertex corrections near the pseudogap QCP without significant finite-size or approximation artifacts that would alter the reported scaling forms.","pith_extraction_headline":"The two-dimensional Hubbard model shows ω/T scaling of the form tanh(ω/2T) in spin and current susceptibilities near its pseudogap quantum critical point."},"references":{"count":125,"sample":[{"doi":"","year":null,"title":"In the strange metal regime this yieldedσ ′ cl,V ≫σ ′ latt,B, i.e","work_id":"9f23d258-21df-4a90-aa67-46f5fd4e1323","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2015,"title":"B. Keimer, S. A. Kivelson, M. R. Norman, S. Uchida, and J. Zaanen, From quantum matter to high- temperature superconductivity in copper oxides, Nature 518, 179 (2015)","work_id":"195b84a0-68ff-49d4-b732-ca4b71005d0a","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1995,"title":"C. Castellani, C. Di Castro, and M. Grilli, Singular quasiparticle scattering in the proximity of charge in- stabilities, Phys. Rev. Lett.75, 4650 (1995)","work_id":"b50b0a56-a35b-46eb-9700-fa63ba291ee4","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1997,"title":"C.M.Varma,Non-Fermi-liquidstatesandpairinginsta- bilityofageneralmodelofcopperoxidemetals,Physical Review B55, 14554 (1997)","work_id":"fb41a8af-3e33-4c4e-84bc-d199ea92be95","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1999,"title":"C. M. Varma, Pseudogap phase and the quantum- critical point in copper-oxide metals, Physical Review Letters83, 3538 (1999)","work_id":"db0fc6e5-ff0d-4210-be46-a76a56d5fb9e","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":125,"snapshot_sha256":"f247c73c38ccd0f2ceecdb16e9dc97335eda66b0ebe0f16c69d076ba2b56a24b","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"43881aa76c0db37b2178c2ceb6033450947b977a91c80225cac927d35e06bb96"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}