Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2110.07969

Kibble Zurek mechanism in rapidly quenched phase transition dynamics

Chuan-Yin Xia, Hua-Bi Zeng

Published Oct 15, 2021• 3 citations
arXivHTMLPDF

Abstract

We propose a theory to explain the experimental observed deviation from the Kibble-Zurek mechanism (KZM) scaling in rapidly quenched critical phase transition dynamics. There is a critical quench rate $τ_{Q}^{c1}$ above it the KZM scaling begins to appear. Smaller than $τ_Q^{c1}$, the defect density $n$ is a constant independent of the quench rate but depends on the final temperature $T_f$ as $n \propto L^d ε_{T_f} ^{d ν}$, the freeze out time $\hat{t}$ admits the scaling law $\hat{t} \propto ε_{T_f}^{-νz}$ where $d$ is the spatial dimension, $ε_{T_f}= (1-T_f/T_c)$ is the dimensionless reduced temperature, $L$ is the sample size, $ν$ and $z$ are spatial and dynamical critical exponents. Quench from $T_c$, the critical rate is determined by the final temperature $T_f$ as $τ_Q^{c1} \propto ε_{T_f}^{-(1+z ν)} $. All the scaling laws are verified in a rapidly quenched superconducting ring via the AdS/CFT correspondence.

DOI
10.48550/arxiv.2110.07969

Related papers

Universal Breakdown of Kibble-Zurek Scaling in Fast Quenches across a Phase Transition

Hua-Bi Zeng, Chuan-Yin Xia, Adolfo del Campo

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.

arXiv:2204.13529•Physical Review Letters•Feb 9, 2023•56 citations

Verified Universal Breakdown of Kibble-Zurek Scaling in Fast Quenches

Xinxin Rao, Liu, Yang, M. Li +3 more

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 \( v_c \) that scales with the quench range \( δ_{\max} \), separating two distinct dynamical regimes. In the Rice-Mele model, for \( v < v_c \), the defect density follows the KZM scaling \( \sim v^{1/2} \); for \( v > v_c \), it exhibits a universal scaling \( \sim δ_{\max} \), independent of the quench rate. Our results provide direct experimental evidence of the predicted breakdown of KZM universality under fast quenches.

arXiv:2506.06841•Jun 7, 2025•0 citations

Quench in 1D Bose-Hubbard Model: Topological Defects and Excitations from Kosterlitz-Thouless Phase Transition Dynamics

Jacek Dziarmaga, Wojciech Hubert Zurek

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.

arXiv:1312.5139•Dec 18, 2013•1 citation

Quench in the 1D Bose-Hubbard model: Topological defects and excitations from the Kosterlitz-Thouless phase transition dynamics

Jacek Dziarmaga, Wojciech Hubert Zurek

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.

Scientific Reports•Aug 5, 2014•31 citations

Universal defect density scaling in an oscillating dynamic phase transition

Wei-Can Yang, Makoto Tsubota, Adolfo del Campo +1 more

Universal scaling laws govern the density of topological defects generated while crossing an equilibrium continuous phase transition. The Kibble-Zurek mechanism (KZM) predicts the dependence on the quench time for slow quenches. By contrast, for fast quenches, the defect density scales universally with the amplitude of the quench. We show that universal scaling laws apply to dynamic phase transitions driven by an oscillating external field. The difference in the energy response of the system to a periodic potential field leads to energy absorption, spontaneous breaking of symmetry, and its restoration. We verify the associated universal scaling laws, providing evidence that the critical behavior of nonequilibrium phase transitions can be described by time-average critical exponents combined with the KZM. Our results demonstrate that the universality of critical dynamics extends beyond equilibrium criticality, facilitating the understanding of complex nonequilibrium systems.

arXiv:2306.03803•Physical review. B./Physical review. B•Nov 30, 2023•7 citations

Deconstructing symmetry breaking dynamics

Fumika Suzuki, Wojciech H. Zurek

The Kibble-Zurek mechanism (KZM) successfully predicts the density of topological defects deposited by the phase transitions, but it is not clear why. Its key conjecture is that, near the critical point of the second-order phase transition, critical slowing down will result in a period when the system is too sluggish to follow the potential that is changing faster than its reaction time. The correlation length at the freeze-out instant $\hat t$ when the order parameter catches up with the post-transition broken symmetry configuration is then decisive, determining when the mosaic of broken symmetry domains locks in topological defects. To understand why the KZM works so well we analyze Landau-Ginzburg model and show why temporal evolution of the order parameter plays such a key role. The analytical solutions we obtain suggest novel, hitherto unexplored, experimentally accessible observables that can shed light on symmetry breaking dynamics while testing the conjecture on which the KZM is based.

cond-mat.stat-mechCross-listedarXiv:2511.22583•Proceedings of the National Academy of Sciences•Nov 28, 2025•3 citations
We propose a theory to explain the experimental observed deviation from the Kibble-Zurek mechanism (KZM) scaling in rapidly quenched critical phase transition dynamics. There is a critical quench rate τQc1τ_{Q}^{c1}τQc1​ above it the KZM scaling begins to appear. Smaller than τQc1τ_Q^{c1}τQc1​, the defect density nnn is a constant independent of the quench rate but depends on the final temperature TfT_fTf​ as n∝LdεTfdνn \propto L^d ε_{T_f} ^{d ν}n∝LdεTf​dν​, the freeze out time t^\hat{t}t^ admits the scaling law t^∝εTf−νz\hat{t} \propto ε_{T_f}^{-νz}t^∝εTf​−νz​ where ddd is the spatial dimension, εTf=(1−Tf/Tc)ε_{T_f}= (1-T_f/T_c)εTf​​=(1−Tf​/Tc​) is the dimensionless reduced temperature, LLL is the sample size, ννν and zzz are spatial and dynamical critical exponents. Quench from TcT_cTc​, the critical rate is determined by the final temperature TfT_fTf​ as τQc1∝εTf−(1+zν)τ_Q^{c1} \propto ε_{T_f}^{-(1+z ν)} τQc1​∝εTf​−(1+zν)​. All the scaling laws are verified in a rapidly quenched superconducting ring via the AdS/CFT correspondence.
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.
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.
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.
Universal scaling laws govern the density of topological defects generated while crossing an equilibrium continuous phase transition. The Kibble-Zurek mechanism (KZM) predicts the dependence on the quench time for slow quenches. By contrast, for fast quenches, the defect density scales universally with the amplitude of the quench. We show that universal scaling laws apply to dynamic phase transitions driven by an oscillating external field. The difference in the energy response of the system to a periodic potential field leads to energy absorption, spontaneous breaking of symmetry, and its restoration. We verify the associated universal scaling laws, providing evidence that the critical behavior of nonequilibrium phase transitions can be described by time-average critical exponents combined with the KZM. Our results demonstrate that the universality of critical dynamics extends beyond equilibrium criticality, facilitating the understanding of complex nonequilibrium systems.
The Kibble-Zurek mechanism (KZM) successfully predicts the density of topological defects deposited by the phase transitions, but it is not clear why. Its key conjecture is that, near the critical point of the second-order phase transition, critical slowing down will result in a period when the system is too sluggish to follow the potential that is changing faster than its reaction time. The correlation length at the freeze-out instant t^\hat tt^ when the order parameter catches up with the post-transition broken symmetry configuration is then decisive, determining when the mosaic of broken symmetry domains locks in topological defects. To understand why the KZM works so well we analyze Landau-Ginzburg model and show why temporal evolution of the order parameter plays such a key role. The analytical solutions we obtain suggest novel, hitherto unexplored, experimentally accessible observables that can shed light on symmetry breaking dynamics while testing the conjecture on which the KZM is based.