{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,12]],"date-time":"2026-03-12T09:23:22Z","timestamp":1773307402414,"version":"3.50.1"},"reference-count":42,"publisher":"AIP Publishing","issue":"11","license":[{"start":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T00:00:00Z","timestamp":1773187200000},"content-version":"vor","delay-in-days":130,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"FCT","award":["UIDB\/04650"],"award-info":[{"award-number":["UIDB\/04650"]}]},{"name":"Center of Physics of University of Minho and University of Porto","award":["UID\/04540"],"award-info":[{"award-number":["UID\/04540"]}]},{"name":"Center of Physics and Engineering of Advanced Materials","award":["LA\/P\/0095\/2020"],"award-info":[{"award-number":["LA\/P\/0095\/2020"]}]},{"name":"LaPMET, Laboratory of Physics for Materials and Emerging Technologies"}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2025,11,1]]},"abstract":"<jats:p>The one-dimensional (1D) Hubbard model at zero magnetic field, h=0, and zero chemical potential, \u03bc=0, and, thus, at the h=\u03bc=0[SO(4)\u00d7U(1)]\/Z2-symmetry point, is the paradigmatic quantum system for low-dimensional strongly correlated electron 1D Mott\u2013Hubbard insulators. Studies relying on hydrodynamic theory and Kardar\u2013Parisi\u2013Zhang (KPZ) scaling have found that for the 1D Hubbard model at the h=\u03bc=0 point, both spin and charge transports are for all temperatures T&amp;gt;0 that are anomalous superdiffusive. In this paper, we review recent results that correct the hydrodynamic theory and KPZ scaling prediction concerning the finite-temperature charge transport, as it is normal diffusive for all finite temperatures T&amp;gt;0. This failure of the hydrodynamic theory and KPZ scaling stems from the misleading assumption that the h=\u03bc=0[SO(4)\u00d7U(1)]\/Z2-symmetry point rather is a h=\u03bc=0SO(4)-symmetry point. Such an assumption has ignored the quantum effects associated with the \u03c4-translational U(1) symmetry beyond SO(4).<\/jats:p>","DOI":"10.1063\/5.0284444","type":"journal-article","created":{"date-parts":[[2025,11,3]],"date-time":"2025-11-03T13:48:51Z","timestamp":1762177731000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Finite-temperature spin and charge transport in integrable one-dimensional Mott\u2013Hubbard insulators"],"prefix":"10.1063","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5624-6294","authenticated-orcid":false,"given":"J. M. 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