Saved in:
Bibliographic Details
Main Authors: Shu, Yu-Rong, Yang, Li-Ying, Yin, Shuai
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2503.16796
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866918437097308160
author Shu, Yu-Rong
Yang, Li-Ying
Yin, Shuai
author_facet Shu, Yu-Rong
Yang, Li-Ying
Yin, Shuai
contents 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 $ζ_d\propto v^{-z/r}$ and $ζ_d'\propto v^{-z/r'}$, 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 $ϕ_q$ shows remarkably distinct scaling behaviors controlled by both FTS regions. For small $v$, $ϕ_q$ is dominated by the time scale $ζ_d$, whereas for large $v$, $ϕ_q$ is governed by the second time scale $ζ_d'$. 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.
format Preprint
id arxiv_https___arxiv_org_abs_2503_16796
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Finite-time scaling with two characteristic time scales: Driven critical dynamics with emergent symmetry
Shu, Yu-Rong
Yang, Li-Ying
Yin, Shuai
Strongly Correlated Electrons
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 $ζ_d\propto v^{-z/r}$ and $ζ_d'\propto v^{-z/r'}$, 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 $ϕ_q$ shows remarkably distinct scaling behaviors controlled by both FTS regions. For small $v$, $ϕ_q$ is dominated by the time scale $ζ_d$, whereas for large $v$, $ϕ_q$ is governed by the second time scale $ζ_d'$. 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.
title Finite-time scaling with two characteristic time scales: Driven critical dynamics with emergent symmetry
topic Strongly Correlated Electrons
url https://arxiv.org/abs/2503.16796