{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,19]],"date-time":"2026-05-19T12:12:04Z","timestamp":1779192724834,"version":"3.51.4"},"reference-count":61,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T00:00:00Z","timestamp":1775001600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"},{"start":{"date-parts":[[2026,5,19]],"date-time":"2026-05-19T00:00:00Z","timestamp":1779148800000},"content-version":"vor","delay-in-days":48,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"}],"funder":[{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"publisher","award":["NRF-RS-2023-00246909"],"award-info":[{"award-number":["NRF-RS-2023-00246909"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Sci Rep"],"DOI":"10.1038\/s41598-026-46239-w","type":"journal-article","created":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T12:48:20Z","timestamp":1775047700000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Non-Fermi liquid of extended range at zero temperature without quantum criticality"],"prefix":"10.1038","volume":"16","author":[{"given":"Tae-Ho","family":"Park","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Han-Yong","family":"Choi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,4,1]]},"reference":[{"key":"46239_CR1","doi-asserted-by":"publisher","first-page":"eabh4273","DOI":"10.1126\/science.abh4273","volume":"377","author":"PW Phillips","year":"2022","unstructured":"Phillips, P. W., Hussey, N. E. & Abbamonte, P. Stranger than metals. Science 377, eabh4273. https:\/\/doi.org\/10.1126\/science.abh4273 (2022).","journal-title":"Science"},{"key":"46239_CR2","doi-asserted-by":"publisher","first-page":"409","DOI":"10.1146\/annurev-conmatphys-031218-013210","volume":"10","author":"C Proust","year":"2019","unstructured":"Proust, C. & Taillefer, L. The remarkable underlying ground states of cuprate superconductors. Annual Review of Condensed Matter Physics 10, 409. https:\/\/doi.org\/10.1146\/annurev-conmatphys-031218-013210 (2019).","journal-title":"Annual Review of Condensed Matter Physics"},{"key":"46239_CR3","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.92.031001","volume":"92","author":"CM Varma","year":"2020","unstructured":"Varma, C. M. Colloquium: Linear in temperature resistivity and associated mysteries including high temperature superconductivity. Rev. Mod. Phys. 92, 031001. https:\/\/doi.org\/10.1103\/RevModPhys.92.031001 (2020).","journal-title":"Rev. Mod. Phys."},{"key":"46239_CR4","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.94.035004","volume":"94","author":"D Chowdhury","year":"2022","unstructured":"Chowdhury, D., Georges, A., Parcollet, O. & Sachdev, S. Sachdev-ye-kitaev models and beyond: Window into non-fermi liquids. Rev. Mod. Phys. 94, 035004. https:\/\/doi.org\/10.1103\/RevModPhys.94.035004 (2022).","journal-title":"Rev. Mod. Phys."},{"key":"46239_CR5","doi-asserted-by":"publisher","first-page":"227","DOI":"10.1146\/annurev-conmatphys-031016-025531","volume":"9","author":"S-S Lee","year":"2018","unstructured":"Lee, S.-S. Recent developments in non-fermi liquid theory. Annual Review of Condensed Matter Physics 9, 227. https:\/\/doi.org\/10.1146\/annurev-conmatphys-031016-025531 (2018).","journal-title":"Annual Review of Condensed Matter Physics"},{"key":"46239_CR6","doi-asserted-by":"publisher","first-page":"603","DOI":"10.1126\/science.1165015","volume":"323","author":"RA Cooper","year":"2009","unstructured":"Cooper, R. A. et al. Anomalous criticality in the electrical resistivity of $$\\text{ La}_{2--x}\\text{ Sr}_x\\text{ CuO}_4$$. Science 323, 603. https:\/\/doi.org\/10.1126\/science.1165015 (2009).","journal-title":"Science"},{"key":"46239_CR7","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1038\/s41567-022-01894-4","volume":"19","author":"X Jiang","year":"2023","unstructured":"Jiang, X. et al. Interplay between superconductivity and the strange-metal state in fese. Nature Physics 19, 365. https:\/\/doi.org\/10.1038\/s41567-022-01894-4 (2023).","journal-title":"Nature Physics"},{"key":"46239_CR8","doi-asserted-by":"publisher","first-page":"661","DOI":"10.1038\/s41586-021-03622-z","volume":"595","author":"J Ayres","year":"2021","unstructured":"Ayres, J. et al. Incoherent transport across the strange-metal regime of overdoped cuprates. Nature 595, 661. https:\/\/doi.org\/10.1038\/s41586-021-03622-z (2021).","journal-title":"Nature"},{"key":"46239_CR9","doi-asserted-by":"publisher","first-page":"205","DOI":"10.1038\/s41586-021-04239-y","volume":"601","author":"C Yang","year":"2022","unstructured":"Yang, C. et al. Signatures of a strange metal in a bosonic system. Nature 601, 205. https:\/\/doi.org\/10.1038\/s41586-021-04239-y (2022).","journal-title":"Nature"},{"key":"46239_CR10","doi-asserted-by":"publisher","first-page":"506","DOI":"10.1126\/science.1262054","volume":"349","author":"T Tomita","year":"2015","unstructured":"Tomita, T., Kuga, K., Uwatoko, Y., Coleman, P. & Nakatsuji, S. Strange metal without magnetic criticality. Science 349, 506. https:\/\/doi.org\/10.1126\/science.1262054 (2015).","journal-title":"Science"},{"key":"46239_CR11","doi-asserted-by":"publisher","first-page":"1871","DOI":"10.1126\/science.1142644","volume":"316","author":"C Pfleiderer","year":"2007","unstructured":"Pfleiderer, C., B\u00f6ni, P., Keller, T., R\u00f6\u00dfler, U. K. & Rosch, A. Non-fermi liquid metal without quantum criticality. Science 316, 1871. https:\/\/doi.org\/10.1126\/science.1142644 (2007).","journal-title":"Science"},{"key":"46239_CR12","doi-asserted-by":"publisher","first-page":"7160","DOI":"10.1073\/pnas.1305240110","volume":"110","author":"T Hu","year":"2013","unstructured":"Hu, T. et al. Non-fermi liquid regimes with and without quantum criticality in $$\\text{ Ce}_{1-x}\\text{ Yb}_x\\text{ CoIn}_5$$. Proceedings of the National Academy of Sciences 110, 7160. https:\/\/doi.org\/10.1073\/pnas.1305240110 (2013).","journal-title":"Proceedings of the National Academy of Sciences"},{"key":"46239_CR13","doi-asserted-by":"publisher","first-page":"1099","DOI":"10.1126\/science.aaw8850","volume":"366","author":"S-D Chen","year":"2019","unstructured":"Chen, S.-D. et al. Incoherent strange metal sharply bounded by a critical doping in bi2212. Science 366, 1099 (2019).","journal-title":"Science"},{"key":"46239_CR14","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevResearch.6.023194","volume":"6","author":"M Qin","year":"2024","unstructured":"Qin, M. et al. Doping dependence of scattering rate for linear-in-temperature resistivity in cuprate superconductors. Phys. Rev. Res. 6, 023194. https:\/\/doi.org\/10.1103\/PhysRevResearch.6.023194 (2024).","journal-title":"Phys. Rev. Res."},{"key":"46239_CR15","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2115819119","volume":"119","author":"W Wu","year":"2022","unstructured":"Wu, W., Wang, X. & Tremblay, A.-M. Non-fermi liquid phase and linear-in-temperature scattering rate in overdoped two-dimensional hubbard model. Proceedings of the National Academy of Sciences 119, e2115819119. https:\/\/doi.org\/10.1073\/pnas.2115819119 (2022).","journal-title":"Proceedings of the National Academy of Sciences"},{"key":"46239_CR16","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.132.236501","volume":"132","author":"N Bashan","year":"2024","unstructured":"Bashan, N., Tulipman, E., Schmalian, J. & Berg, E. Tunable non-fermi liquid phase from coupling to two-level systems. Phys. Rev. Lett. 132, 236501. https:\/\/doi.org\/10.1103\/PhysRevLett.132.236501 (2024).","journal-title":"Phys. Rev. Lett."},{"key":"46239_CR17","doi-asserted-by":"publisher","first-page":"1354707","DOI":"10.1016\/j.physc.2025.1354707","volume":"633","author":"S Sachdev","year":"2025","unstructured":"Sachdev, S. The foot, the fan, and the cuprate phase diagram: Fermi-volume-changing quantum phase transitions. Physica C: Superconductivity and its Applications 633, 1354707. https:\/\/doi.org\/10.1016\/j.physc.2025.1354707 (2025).","journal-title":"Physica C: Superconductivity and its Applications"},{"key":"46239_CR18","doi-asserted-by":"publisher","first-page":"L121110","DOI":"10.1103\/PhysRevB.110.L121110","volume":"110","author":"PA Lee","year":"2024","unstructured":"Lee, P. A. Model of a non-fermi liquid with power-law resistivity: Strange metal with a not-so-strange origin. Phys. Rev. B 110, L121110. https:\/\/doi.org\/10.1103\/PhysRevB.110.L121110 (2024).","journal-title":"Phys. Rev. B"},{"key":"46239_CR19","doi-asserted-by":"publisher","DOI":"10.3389\/fphy.2022.1021462","author":"J Ayres","year":"2022","unstructured":"Ayres, J., Katsnelson, M. I. & Hussey, N. E. Superfluid density and two-component conductivity in hole-doped cuprates. Frontiers in Physics https:\/\/doi.org\/10.3389\/fphy.2022.1021462 (2022).","journal-title":"Frontiers in Physics"},{"key":"46239_CR20","doi-asserted-by":"publisher","first-page":"1354362","DOI":"10.1016\/j.physc.2023.1354362","volume":"614","author":"N Hussey","year":"2023","unstructured":"Hussey, N. High-temperature superconductivity and strange metallicity: Simple observations with (possibly) profound implications. Physica C: Superconductivity and its Applications 614, 1354362. https:\/\/doi.org\/10.1016\/j.physc.2023.1354362 (2023).","journal-title":"Physica C: Superconductivity and its Applications"},{"key":"46239_CR21","doi-asserted-by":"publisher","first-page":"309","DOI":"10.1038\/nature19061","volume":"536","author":"I Bozovic","year":"2016","unstructured":"Bozovic, I., He, X., Wu, J. & Bollinger, A. T. Dependence of the critical temperature in overdoped copper oxides on superfluid density. Nature 536, 309. https:\/\/doi.org\/10.1038\/nature19061 (2016).","journal-title":"Nature"},{"key":"46239_CR22","doi-asserted-by":"publisher","first-page":"30","DOI":"10.1016\/j.physc.2018.02.055","volume":"558","author":"I Bo\u017eovi\u0107","year":"2019","unstructured":"Bo\u017eovi\u0107, I., Wu, J., He, X. & Bollinger, A. What is really extraordinary in cuprate superconductors?. Physica C: Superconductivity and its Applications 558, 30. https:\/\/doi.org\/10.1016\/j.physc.2018.02.055 (2019).","journal-title":"Physica C: Superconductivity and its Applications"},{"key":"46239_CR23","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.103.235156","volume":"103","author":"B Nosarzewski","year":"2021","unstructured":"Nosarzewski, B. et al. Superconductivity, charge density waves, and bipolarons in the holstein model. Phys. Rev. B 103, 235156. https:\/\/doi.org\/10.1103\/PhysRevB.103.235156 (2021).","journal-title":"Phys. Rev. B"},{"key":"46239_CR24","doi-asserted-by":"publisher","first-page":"311","DOI":"10.1038\/s42005-022-01092-x","volume":"5","author":"S Karakuzu","year":"2022","unstructured":"Karakuzu, S. et al. Stripe correlations in the two-dimensional hubbard-holstein model. Communications Physics 5, 311. https:\/\/doi.org\/10.1038\/s42005-022-01092-x (2022).","journal-title":"Communications Physics"},{"key":"46239_CR25","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1038\/s41535-023-00553-y","volume":"8","author":"O Bradley","year":"2023","unstructured":"Bradley, O., Cohen-Stead, B., Johnston, S., Barros, K. & Scalettar, R. T. Charge order in the kagome lattice holstein model: a hybrid monte carlo study. npj Quantum Materials 8, 21. https:\/\/doi.org\/10.1038\/s41535-023-00553-y (2023).","journal-title":"npj Quantum Materials"},{"key":"46239_CR26","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.111.155140","volume":"111","author":"G Issa","year":"2025","unstructured":"Issa, G., Bradley, O., Khatami, E. & Scalettar, R. Learning by confusion: The phase diagram of the holstein model. Phys. Rev. B 111, 155140. https:\/\/doi.org\/10.1103\/PhysRevB.111.155140 (2025).","journal-title":"Phys. Rev. B"},{"key":"46239_CR27","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.98.085405","volume":"98","author":"M Weber","year":"2018","unstructured":"Weber, M. & Hohenadler, M. Two-dimensional holstein-hubbard model: Critical temperature, ising universality, and bipolaron liquid. Phys. Rev. B 98, 085405. https:\/\/doi.org\/10.1103\/PhysRevB.98.085405 (2018).","journal-title":"Phys. Rev. B"},{"key":"46239_CR28","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1038\/s41535-022-00426-w","volume":"7","author":"KS Huang","year":"2022","unstructured":"Huang, K. S., Han, Z., Kivelson, S. A. & Yao, H. Pair-density-wave in the strong coupling limit of the holstein-hubbard model. npj Quantum Materials 7, 17. https:\/\/doi.org\/10.1038\/s41535-022-00426-w (2022).","journal-title":"npj Quantum Materials"},{"key":"46239_CR29","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.109.246404","volume":"109","author":"EA Nowadnick","year":"2012","unstructured":"Nowadnick, E. A., Johnston, S., Moritz, B., Scalettar, R. T. & Devereaux, T. P. Competition between antiferromagnetic and charge-density-wave order in the half-filled hubbard-holstein model. Phys. Rev. Lett. 109, 246404. https:\/\/doi.org\/10.1103\/PhysRevLett.109.246404 (2012).","journal-title":"Phys. Rev. Lett."},{"key":"46239_CR30","doi-asserted-by":"publisher","first-page":"80","DOI":"10.1038\/s42005-020-0342-2","volume":"3","author":"NC Costa","year":"2020","unstructured":"Costa, N. C., Seki, K., Yunoki, S. & Sorella, S. Phase diagram of the two-dimensional hubbard-holstein model. Communications Physics 3, 80. https:\/\/doi.org\/10.1038\/s42005-020-0342-2 (2020).","journal-title":"Communications Physics"},{"key":"46239_CR31","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.70.125114","volume":"70","author":"GS Jeon","year":"2004","unstructured":"Jeon, G. S., Park, T.-H., Han, J. H., Lee, H. C. & Choi, H.-Y. Dynamical mean-field theory of the hubbard-holstein model at half filling: Zero temperature metal-insulator and insulator-insulator transitions. Phys. Rev. B 70, 125114. https:\/\/doi.org\/10.1103\/PhysRevB.70.125114 (2004).","journal-title":"Phys. Rev. B"},{"key":"46239_CR32","doi-asserted-by":"publisher","first-page":"14320","DOI":"10.1103\/PhysRevB.58.14320","volume":"58","author":"P Benedetti","year":"1998","unstructured":"Benedetti, P. & Zeyher, R. Holstein model in infinite dimensions at half-filling. Phys. Rev. B 58, 14320. https:\/\/doi.org\/10.1103\/PhysRevB.58.14320 (1998).","journal-title":"Phys. Rev. B"},{"key":"46239_CR33","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.89.196401","volume":"89","author":"D Meyer","year":"2002","unstructured":"Meyer, D., Hewson, A. C. & Bulla, R. Gap formation and soft phonon mode in the holstein model. Phys. Rev. Lett. 89, 196401. https:\/\/doi.org\/10.1103\/PhysRevLett.89.196401 (2002).","journal-title":"Phys. Rev. Lett."},{"key":"46239_CR34","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.91.186405","volume":"91","author":"M Capone","year":"2003","unstructured":"Capone, M. & Ciuchi, S. Polaron crossover and bipolaronic metal-insulator transition in the half-filled holstein model. Phys. Rev. Lett. 91, 186405. https:\/\/doi.org\/10.1103\/PhysRevLett.91.186405 (2003).","journal-title":"Phys. Rev. Lett."},{"key":"46239_CR35","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.70.155103","volume":"70","author":"W Koller","year":"2004","unstructured":"Koller, W., Meyer, D. & Hewson, A. C. Dynamic response functions for the holstein-hubbard model. Phys. Rev. B 70, 155103. https:\/\/doi.org\/10.1103\/PhysRevB.70.155103 (2004).","journal-title":"Phys. Rev. B"},{"key":"46239_CR36","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1103\/RevModPhys.68.13","volume":"68","author":"A Georges","year":"1996","unstructured":"Georges, A., Kotliar, G., Krauth, W. & Rozenberg, M. J. Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions. Rev. Mod. Phys. 68, 13. https:\/\/doi.org\/10.1103\/RevModPhys.68.13 (1996).","journal-title":"Rev. Mod. Phys."},{"key":"46239_CR37","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.87.075149","volume":"87","author":"M Hohenadler","year":"2013","unstructured":"Hohenadler, M. & Assaad, F. F. Excitation spectra and spin gap of the half-filled holstein-hubbard model. Phys. Rev. B 87, 075149. https:\/\/doi.org\/10.1103\/PhysRevB.87.075149 (2013).","journal-title":"Phys. Rev. B"},{"key":"46239_CR38","doi-asserted-by":"publisher","first-page":"12133","DOI":"10.1103\/PhysRevB.53.12133","volume":"53","author":"L Balents","year":"1996","unstructured":"Balents, L. & Fisher, M. P. A. Weak-coupling phase diagram of the two-chain hubbard model. Phys. Rev. B 53, 12133. https:\/\/doi.org\/10.1103\/PhysRevB.53.12133 (1996).","journal-title":"Phys. Rev. B"},{"key":"46239_CR39","unstructured":"See Supplementary Information"},{"key":"46239_CR40","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.122.027003","volume":"122","author":"F Mahmood","year":"2019","unstructured":"Mahmood, F., He, X., Bo\u017eovi\u0107, I. & Armitage, N. P. Locating the missing superconducting electrons in the overdoped cuprates $${\\rm la}_{2-x}{\\rm sr}_{x}{\\rm cuo}_{4}$$. Phys. Rev. Lett. 122, 027003. https:\/\/doi.org\/10.1103\/PhysRevLett.122.027003 (2019).","journal-title":"Phys. Rev. Lett."},{"key":"46239_CR41","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1007\/s40509-017-0126-x","volume":"5","author":"I Bo\u017eovi\u0107","year":"2018","unstructured":"Bo\u017eovi\u0107, I., Wu, J., He, X. & Bollinger, A. T. Is there a path from cuprates towards room-temperature superconductivity?. Quantum Studies: Mathematics and Foundations 5, 55. https:\/\/doi.org\/10.1007\/s40509-017-0126-x (2018).","journal-title":"Quantum Studies: Mathematics and Foundations"},{"key":"46239_CR42","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.64.045103","volume":"64","author":"R Bulla","year":"2001","unstructured":"Bulla, R., Costi, T. A. & Vollhardt, D. Finite-temperature numerical renormalization group study of the mott transition. Phys. Rev. B 64, 045103. https:\/\/doi.org\/10.1103\/PhysRevB.64.045103 (2001).","journal-title":"Phys. Rev. B"},{"key":"46239_CR43","doi-asserted-by":"publisher","DOI":"10.1038\/s41535-020-00266-6","author":"XY Xu","year":"2020","unstructured":"Xu, X. Y., Klein, A., Sun, K., Chubukov, A. V. & Meng, Z. Y. Identification of non-fermi liquid fermionic self-energy from quantum monte carlo data. npj. Quantum Materials https:\/\/doi.org\/10.1038\/s41535-020-00266-6 (2020).","journal-title":"npj. Quantum Materials"},{"key":"46239_CR44","doi-asserted-by":"publisher","first-page":"4612","DOI":"10.1103\/PhysRevLett.86.4612","volume":"86","author":"M Keller","year":"2001","unstructured":"Keller, M., Metzner, W. & Schollw\u00f6ck, U. Dynamical mean-field theory for pairing and spin gap in the attractive hubbard model. Phys. Rev. Lett. 86, 4612. https:\/\/doi.org\/10.1103\/PhysRevLett.86.4612 (2001).","journal-title":"Phys. Rev. Lett."},{"key":"46239_CR45","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.88.126403","volume":"88","author":"M Capone","year":"2002","unstructured":"Capone, M., Castellani, C. & Grilli, M. First-order pairing transition and single-particle spectral function in the attractive hubbard model. Phys. Rev. Lett. 88, 126403. https:\/\/doi.org\/10.1103\/PhysRevLett.88.126403 (2002).","journal-title":"Phys. Rev. Lett."},{"key":"46239_CR46","doi-asserted-by":"publisher","DOI":"10.1143\/JPSJ.81.064718","volume":"81","author":"S Tamura","year":"2012","unstructured":"Tamura, S. & Yokoyama, H. Variational monte carlo study of spin-gapped normal state and bcs\u2013bec crossover in two-dimensional attractive hubbard model. Journal of the Physical Society of Japan 81, 064718. https:\/\/doi.org\/10.1143\/JPSJ.81.064718 (2012).","journal-title":"Journal of the Physical Society of Japan"},{"key":"46239_CR47","doi-asserted-by":"crossref","unstructured":"Toschi, A., Barone, P., Capone, M., & Castellani, C. Pairing and superconductivity from weak to strong coupling in the attractive hubbard model. New J. Phys. 7 7. (2025).","DOI":"10.1088\/1367-2630\/7\/1\/007"},{"key":"46239_CR48","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.72.235118","volume":"72","author":"A Toschi","year":"2005","unstructured":"Toschi, A., Capone, M. & Castellani, C. Energetic balance of the superconducting transition across the bcs\u2013bose einstein crossover in the attractive hubbard model. Phys. Rev. B 72, 235118. https:\/\/doi.org\/10.1103\/PhysRevB.72.235118 (2005).","journal-title":"Phys. Rev. B"},{"key":"46239_CR49","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.21.1044","volume":"21","author":"HR Krishna-murthy","year":"1980","unstructured":"H. R. Krishna-murthy, J. W. Wilkins, and K. G. Wilson, Renormalization-group approach to the andersonmodel of dilute magnetic alloys. ii. static properties forthe asymmetric case. Phys. Rev. B 21, 1044 (1980).","journal-title":"Phys. Rev. B"},{"key":"46239_CR50","doi-asserted-by":"publisher","first-page":"8406","DOI":"10.1038\/s41467-024-52564-3","volume":"15","author":"J Ayres","year":"2024","unstructured":"Ayres, J. et al. Universal correlation between h-linear magnetoresistance and t-linear resistivity in high-temperature superconductors. Nature Communications 15, 8406. https:\/\/doi.org\/10.1038\/s41467-024-52564-3 (2024).","journal-title":"Nature Communications"},{"key":"46239_CR51","doi-asserted-by":"publisher","first-page":"194","DOI":"10.1038\/nphys2869","volume":"10","author":"JG Analytis","year":"2014","unstructured":"Analytis, J. G. et al. Transport near a quantum critical point in bafe2(as1-xpx)2. Nature Physics 10, 194. https:\/\/doi.org\/10.1038\/nphys2869 (2014).","journal-title":"Nature Physics"},{"key":"46239_CR52","doi-asserted-by":"publisher","first-page":"916","DOI":"10.1038\/nphys3773","volume":"12","author":"IM Hayes","year":"2016","unstructured":"Hayes, I. M. et al. Scaling between magnetic field and temperature in the high-temperature superconductor bafe2(as1-xpx)2. Nature Physics 12, 916. https:\/\/doi.org\/10.1038\/nphys3773 (2016).","journal-title":"Nature Physics"},{"key":"46239_CR53","doi-asserted-by":"publisher","first-page":"3116","DOI":"10.1038\/s41467-023-38763-4","volume":"14","author":"S Cai","year":"2023","unstructured":"Cai, S. et al. The breakdown of both strange metal and superconducting states at a pressure-induced quantum critical point in iron-pnictide superconductors. Nature Communications 14, 3116. https:\/\/doi.org\/10.1038\/s41467-023-38763-4 (2023).","journal-title":"Nature Communications"},{"key":"46239_CR54","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.124.076801","volume":"124","author":"Y Cao","year":"2020","unstructured":"Cao, Y. et al. Strange metal in magic-angle graphene with near planckian dissipation. Phys. Rev. Lett. 124, 076801. https:\/\/doi.org\/10.1103\/PhysRevLett.124.076801 (2020).","journal-title":"Phys. Rev. Lett."},{"key":"46239_CR55","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.127.266601","volume":"127","author":"P Cha","year":"2021","unstructured":"Cha, P., Patel, A. A. & Kim, E.-A. Strange metals from melting correlated insulators in twisted bilayer graphene. Phys. Rev. Lett. 127, 266601. https:\/\/doi.org\/10.1103\/PhysRevLett.127.266601 (2021).","journal-title":"Phys. Rev. Lett."},{"key":"46239_CR56","doi-asserted-by":"crossref","unstructured":"Cai, X., Han, Z., Li, Z.-X., Kivelson, S.\u00a0A., & Yao, H. Quantum spin liquid from electron-phonon coupling. arXiv:2408.04002 (2024).","DOI":"10.1073\/pnas.2426111122"},{"key":"46239_CR57","doi-asserted-by":"publisher","first-page":"2171","DOI":"10.1143\/PTP.48.2171","volume":"48","author":"H Shiba","year":"1972","unstructured":"Shiba, H. Thermodynamic properties of the one-dimensional half-filled-band hubbard model. ii: Application of the grand canonical method. Progress of Theoretical Physics 48, 2171. https:\/\/doi.org\/10.1143\/PTP.48.2171 (1972).","journal-title":"Progress of Theoretical Physics"},{"key":"46239_CR58","doi-asserted-by":"publisher","first-page":"L121109","DOI":"10.1103\/PhysRevB.110.L121109","volume":"110","author":"P-O Downey","year":"2024","unstructured":"Downey, P.-O., Gingras, O., H\u00e9bert, C.-D., Charlebois, M. & Tremblay, A.-M.S. Doping the mott insulating state of the triangular-lattice hubbard model reveals the sordi transition. Phys. Rev. B 110, L121109. https:\/\/doi.org\/10.1103\/PhysRevB.110.L121109 (2024).","journal-title":"Phys. Rev. B"},{"key":"46239_CR59","doi-asserted-by":"publisher","first-page":"22715","DOI":"10.1038\/srep22715","volume":"6","author":"L Fratino","year":"2016","unstructured":"Fratino, L., S\u00e9mon, P., Sordi, G. & Tremblay, A.-M.S. An organizing principle for two-dimensional strongly correlated superconductivity. Scientific Reports 6, 22715. https:\/\/doi.org\/10.1038\/srep22715 (2016).","journal-title":"Scientific Reports"},{"key":"46239_CR60","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.99.174503","volume":"99","author":"T-H Park","year":"2019","unstructured":"Park, T.-H. & Choi, H.-Y. Dynamical effects on superconductivity in a bcs-bec crossover: Dynamical mean field theory and numerical renormalization group study of the holstein model in infinite dimensions. Phys. Rev. B 99, 174503. https:\/\/doi.org\/10.1103\/PhysRevB.99.174503 (2019).","journal-title":"Phys. Rev. B"},{"key":"46239_CR61","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.79.214518","volume":"79","author":"J Bauer","year":"2009","unstructured":"Bauer, J., Hewson, A. C. & Dupuis, N. Dynamical mean-field theory and numerical renormalization group study of superconductivity in the attractive hubbard model. Phys. Rev. B 79, 214518. https:\/\/doi.org\/10.1103\/PhysRevB.79.214518 (2009).","journal-title":"Phys. Rev. B"}],"container-title":["Scientific Reports"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.nature.com\/articles\/s41598-026-46239-w","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41598-026-46239-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41598-026-46239-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,19]],"date-time":"2026-05-19T12:02:30Z","timestamp":1779192150000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.nature.com\/articles\/s41598-026-46239-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4,1]]},"references-count":61,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,12]]}},"alternative-id":["46239"],"URL":"https:\/\/doi.org\/10.1038\/s41598-026-46239-w","relation":{},"ISSN":["2045-2322"],"issn-type":[{"value":"2045-2322","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4,1]]},"assertion":[{"value":"27 November 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 March 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 April 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"15402"}}