Finite-time scaling with two characteristic time scales: Driven critical dynamics with emergent symmetry

[2503.16796] Finite-time scaling with two characteristic time scales: Driven critical dynamics with emergent symmetry Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Condensed Matter > Strongly Correlated Electrons arXiv:2503.16796 (cond-mat) [Submitted on 21 Mar 2025] Title: Finite-time scaling with two characteristic time scales: Driven critical dynamics with emergent symmetry Authors: Yu-Rong Shu , Li-Ying Yang , Shuai Yin View a PDF of the paper titled Finite-time scaling with two characteristic time scales: Driven critical dynamics with emergent symmetry, by Yu-Rong Shu and Li-Ying Yang and Shuai Yin View PDF HTML (experimental) Abstract: Critical points with emergent symmetry exhibit intriguing scaling properties induced by two divergent length scales, attracting extensive investigations recently. We study the driven critical dynamics in a three-dimensional $q$-state clock model, in which the ordered phase breaks the $Z_q$ discrete symmetry, while an emergent $U(1)$ symmetry appears at the critical point. By increasing the temperature at a finite velocity $v$ to traverse the critical point from the ordered phase, we uncover rich dynamic scaling properties beyond the celebrated Kibble-Zurek mechanism. Our findings reveal the existence of two finite-time scaling (FTS) regions, characterized by two driving-induced time scales $\zeta_d\propto v^{-z/r}$ and $\zeta_d'\propto v^{-z/r'}$, respectively. Here $z$ is the dynamic exponent, $r$ is the usual critical exponent of $v$, and $r'$ represents an additional critical exponent of $v$ associated with the dangerously irrelevant scaling variable. While the square of the order parameter $M^2$ obeys the usual FTS form, the angular order parameter $\phi_q$ shows remarkably distinct scaling behaviors controlled by both FTS regions. For small $v$, $\phi_q$ is dominated by the time scale $\zeta_d$, whereas for large $v$, $\phi_q$ is governed by the second time scale $\zeta_d'$. We verify the universality of these scaling properties in models with both isotropic and anisotropic couplings. Our theoretical insights provide a promising foundation for further experimental investigations in the hexagonal RMnO$_3$ (R=rare earth) materials. Comments: 13 pages, 11 figures Subjects: Strongly Correlated Electrons (cond-mat.str-el) Cite as: arXiv:2503.16796 [cond-mat.str-el] (or arXiv:2503.16796v1 [cond-mat.str-el] for this version) https://doi.org/10.48550/arXiv.2503.16796 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Phys. Rev. B 113, 134303 (2026) Related DOI : https://doi.org/10.1103/scjr-r3hj Focus to learn more DOI(s) linking to related resources Submission history From: Yu-Rong Shu [ view email ] [v1] Fri, 21 Mar 2025 02:14:14 UTC (17,729 KB) Full-text links: Access Paper: View a PDF of the paper titled Finite-time scaling with two characteristic time scales: Driven critical dynamics with emergent symmetry, by Yu-Rong Shu and Li-Ying Yang and Shuai Yin View PDF HTML (experimental) TeX Source view license Current browse context: cond-mat.str-el < prev | next > new | recent | 2025-03 Change to browse by: cond-mat References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... 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