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arXiv:2607.20081

Logarithmic scaling correction in quench dynamics of the J1-J2 Potts model

Kun Li, Wanzhou Zhang

Published Jul 22, 2026• 0 citations
arXivHTMLPDF

Abstract

In conventional quench dynamics governed by the Kibble-Zurek mechanism (KZM), the defect density generally decays as a pure power law of the quench rate. However, the KZM scaling of the two-dimensional (2D) XY model with topological phase transitions features prominent logarithmic corrections. Nevertheless, it remains unclear whether such logarithmic scaling corrections emerge in discrete-spin systems that host two successive topological phase transitions under thermal quenches. This work investigates the J1-J2 antiferromagnetic Potts model and constructs its equilibrium phase diagram. Based on the temperature ranges of the paramagnetic phase, quasi-long-range ordered (QLRO) phase, long-range ordered phase, and zero-temperature ground state, we design four quench protocols with distinct temperature intervals. Our results demonstrate that quenches terminating in the QLRO phase exhibit logarithmically corrected KZM scaling of the excess energy density, consistent with the dynamical universality class of the 2D XY model. In contrast, quenches ending in the LRO phase, including both finite-temperature and zero-temperature protocols, follow conventional power-law scaling. Our results clearly uncover the characteristic scaling corrections of the J1-J2 Potts model and offer theoretical guidance for future experimental investigations of KZM via photonic simulation platforms.

DOI
10.48550/arxiv.2607.20081

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In conventional quench dynamics governed by the Kibble-Zurek mechanism (KZM), the defect density generally decays as a pure power law of the quench rate. However, the KZM scaling of the two-dimensional (2D) XY model with topological phase transitions features prominent logarithmic corrections. Nevertheless, it remains unclear whether such logarithmic scaling corrections emerge in discrete-spin systems that host two successive topological phase transitions under thermal quenches. This work investigates the J1-J2 antiferromagnetic Potts model and constructs its equilibrium phase diagram. Based on the temperature ranges of the paramagnetic phase, quasi-long-range ordered (QLRO) phase, long-range ordered phase, and zero-temperature ground state, we design four quench protocols with distinct temperature intervals. Our results demonstrate that quenches terminating in the QLRO phase exhibit logarithmically corrected KZM scaling of the excess energy density, consistent with the dynamical universality class of the 2D XY model. In contrast, quenches ending in the LRO phase, including both finite-temperature and zero-temperature protocols, follow conventional power-law scaling. Our results clearly uncover the characteristic scaling corrections of the J1-J2 Potts model and offer theoretical guidance for future experimental investigations of KZM via photonic simulation platforms.
We investigate the out of equilibrium dynamics of the two-dimensional XY model when cooled across the Berezinskii–Kosterlitz–Thouless (BKT) phase transition using different protocols. We focus on the evolution of the growing correlation length and the density of topological defects (vortices). By using Monte Carlo simulations we first determine the time and temperature dependence of the growing correlation length after an infinitely rapid quench from above the transition temperature to the quasi-long-range order region. The functional form is consistent with a logarithmic correction to the diffusive law and it serves to validate dynamic scaling in this problem. This analysis clarifies the different dynamic roles played by bound and free vortices. We then revisit the Kibble–Zurek mechanism in thermal phase transitions in which the disordered state is plagued with topological defects. We provide a theory of quenching rate dependence in systems with the BKT-type transition that goes beyond the equilibrium scaling arguments. Finally, we discuss the implications of our results for a host of physical systems with vortex excitations, including planar ferromagnets and liquid crystals.
The Kibble-Zurek mechanism (KZM) predicts that when a system is driven through a continuous phase transition, the density of topological defects scales universally with the quench rate. Recent theoretical work [H.-B. Zeng \textit{et al.}, \textit{Phys. Rev. Lett.} \textbf{130}, 060402 (2023)] has challenged this picture, showing that under sufficiently fast quenches, both the defect density and freezing time become independent of the quench rate and instead scale universally with the quench range. Here, we experimentally test this prediction using a single trapped-ion qubit to simulate fast quantum quenches in the Landau-Zener and 1D Rice-Mele models. We identify a critical quench rate vc v_c vc​ that scales with the quench range δmax⁡ δ_{\max} δmax​, separating two distinct dynamical regimes. In the Rice-Mele model, for v<vc v < v_c v<vc​, the defect density follows the KZM scaling ∼v1/2 \sim v^{1/2} ∼v1/2; for v>vc v > v_c v>vc​, it exhibits a universal scaling ∼δmax⁡ \sim δ_{\max} ∼δmax​, independent of the quench rate. Our results provide direct experimental evidence of the predicted breakdown of KZM universality under fast quenches.
Kibble-Zurek mechanism (KZM) uses critical scaling to predict density of topological defects and other excitations created in second order phase transitions. We point out that simply inserting asymptotic critical exponents deduced from the immediate vicinity of the critical point to obtain KZM predictions can lead to results that are inconsistent with a more careful KZM-like analysis based on causality -- on the comparison of the relaxation time of the order parameter with the time "distance" from the critical point. As a result, scaling of quench-generated excitations with quench rates can exhibit behavior that is locally (i.e., in the neighborhood of any given quench rate) well approximated by the power law, but with exponents that depend on that rate, and that are quite different from the naive prediction based on the critical exponents relevant for asymptotically long quench times. Kosterlitz-Thouless scaling (that governs e.g. Mott insulator to superfluid transition in the Bose-Hubbard model in one dimension) is investigated as an example of this phenomenon.
Abstract We study the dynamics of second-order phase transitions that may have taken place in the early universe and analyze the Kibble-Zurek (KZ) scaling as well as the formation of topological defects emerging from a quench in the one-dimensional Bose-Hubbard model. We describe the universal dynamics of the KZ mechanism (KZM) and the topological defect formation by simulating the Bose–Hubbard model at zero temperature. We study the effects of thermalization on the ground state by analyzing the transition between Mott and superfluid phases. The out-of-equilibrium dynamics induced by a quench of the hopping parameter is presented. We find a KZ scaling behaviour at zero temperature and analyze the KZ dynamics.
The crossing of a continuous phase transition gives rise to the formation of topological defects described by the Kibble-Zurek mechanism (KZM) in the limit of slow quenches. The KZM predicts a universal power-law scaling of the defect density as a function of the quench time. We focus on the deviations from KZM experimentally observed in rapid quenches and establish their universality. While KZM scaling holds below a critical quench rate, for faster quenches the defect density and the freeze-out time become independent of the quench rate and exhibit a universal power-law scaling with the final value of the control parameter. These predictions are verified in several paradigmatic scenarios in both the classical and quantum domains.
Kibble-Zurek mechanism (KZM) uses critical scaling to predict density of topological defects and other excitations created in second order phase transitions. We point out that simply inserting asymptotic critical exponents deduced from the immediate vicinity of the critical point to obtain predictions can lead to results that are inconsistent with a more careful KZM analysis based on causality - on the comparison of the relaxation time of the order parameter with the "time distance" from the critical point. As a result, scaling of quench-generated excitations with quench rates can exhibit behavior that is locally (i.e., in the neighborhood of any given quench rate) well approximated by the power law, but with exponents that depend on that rate, and that are quite different from the naive prediction based on the critical exponents relevant for asymptotically long quench times. Kosterlitz-Thouless scaling (that governs e.g. Mott insulator to superfluid transition in the Bose-Hubbard model in one dimension) is investigated as an example of this phenomenon.