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arXiv:2501.01064 · Chinese Physics Letters

Is There Kibble-Zurek Scaling of Topological Defects in First-Order Phase Transitions?

Fan Zhong

Published Feb 13, 2025• 2 citations
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Abstract

Abstract Kibble-Zurek scaling is the scaling of the density of topological defects formed via the Kibble-Zurek mechanism with respect to the rate at which a system is cooled across a continuous phase transition. Recently, the density of the topological defects formed via the Kibble-Zurek mechanism was estimated for a system cooled through a first-order phase transition rather than conventional continuous transitions. Here we address the problem of whether such defects generated across a first-order phase transition exhibit Kibble-Zurek scaling similar to the case in continuous phase transitions. We show that any possible Kibble-Zurek scaling for the topological defects can only be a very rough approximation due to an intrinsic field responsible for the scaling. However, complete universal scaling for other properties does exist.

DOI
10.1088/0256-307x/42/3/030203

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Abstract Kibble-Zurek scaling is the scaling of the density of topological defects formed via the Kibble-Zurek mechanism with respect to the rate at which a system is cooled across a continuous phase transition. Recently, the density of the topological defects formed via the Kibble-Zurek mechanism was estimated for a system cooled through a first-order phase transition rather than conventional continuous transitions. Here we address the problem of whether such defects generated across a first-order phase transition exhibit Kibble-Zurek scaling similar to the case in continuous phase transitions. We show that any possible Kibble-Zurek scaling for the topological defects can only be a very rough approximation due to an intrinsic field responsible for the scaling. However, complete universal scaling for other properties does exist.
The Kibble-Zurek mechanism predicts a universal scaling behavior of the defect production when a system is slowly quenched across a critical phase transition point. Here, we discover that the universal scaling behavior across a higher-order topological phase transition does not conform to the traditional Kibble-Zurek mechanism. To explain the anomalous scaling exponent, we develop a solvable Landau-Zener model that takes into account the role of topological edge band that dominates the phase transition. For a two-dimensional boundary-obstructed higher-order topological system, the Kibble-Zurek scaling must be modified to adopt the effective dimension of topological edge band instead of the real physical dimension. We also find that across the boundary-obstructed higher-order topological phase transition, boundary conditions can drastically modify the scaling behaviors. For comparison, we investigate the slow quench dynamics across the bulk-obstructed phase transitions and a single multicritical point, which obeys the Kibble-Zurek mechanism with physical dimension.
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 the average number of topological defects generated upon crossing a continuous or quantum phase transition obeys a universal scaling law with the quench time. Fluctuations in the defect number near equilibrium are approximately of Gaussian form, in agreement with the central limit theorem. Using large deviations theory, we characterize the universality of fluctuations beyond the KZM and report the exact form of the rate function in the transverse-field quantum Ising model. In addition, we characterize the scaling of large deviations in an arbitrary continuous phase transition, building on recent evidence establishing the universality of the defect number distribution.
The Kibble-Zurek mechanism (KZM) describes the nonequilibrium dynamics and topological defect formation in systems undergoing second-order phase transitions. KZM has found applications in fields such as cosmology and condensed matter physics. However, it is generally not suitable for describing first-order phase transitions. It has been demonstrated that transitions in systems like superconductors or charged superfluids, typically classified as second order, can exhibit weakly first-order characteristics when the influence of fluctuations is taken into account. Moreover, the order of the phase transition (i.e., the extent to which it becomes first rather than second order) can be tuned. We explore quench-induced formation of topological defects in such tunable phase transitions and propose that their density can be predicted by combining KZM with nucleation theory.
The Kibble-Zurek (KZ) mechanism renders a theoretical framework for elucidating the formation of topological defects across continuous phase transitions. Nevertheless, it is not immediately clear whether the KZ mechanism applies to topological phase transitions. The direct experimental study for such a topic is hindered by quenching a certain parameter over orders of magnitude in topological materials. Instead, we investigate the KZ behavior across topological transitions of a Chern band in two-dimensional (2D) optical Raman lattices with quantum gases. Defined as the defects, excitation density is reconstructed via measuring the spin wave functions, with which the power-law scaling of total excitation density is extracted and such scaling could be interpreted within the KZ framework. Our work has heralded the commencement of experimentally exploring the KZ mechanism of the topological phase transitions.
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.