Kibble-Zurek mechanism and finite-time scaling

Yingyi Huang, Shuai Yin, Baoquan Feng, and Fan Zhong
Phys. Rev. B 90, 134108 – Published 28 October 2014

Abstract

The Kibble-Zurek (KZ) mechanism has been applied to a variety of systems ranging from low-temperature Bose-Einstein condensations to grand unification scales in particle physics and cosmology and from classical phase transitions to quantum phase transitions. Here, we show that finite-time scaling (FTS) provides a detailed improved understanding of the mechanism. In particular, the finite time scale, which is introduced by the external driving (or quenching) and results in FTS, is the origin of the division of the adiabatic regimes from the impulse regime in the KZ mechanism. The origin of the KZ scaling for the defect density, generated during the driving through a critical point, is not that the correlation length ceases growing in the nonadiabatic impulse regime, but rather, is that it is taken over by the effective finite length scale corresponding to the finite time scale. We also show that FTS accounts well for and improves the scaling ansatz proposed recently by Liu, Polkovnikov, and Sandvik, [Phys. Rev. B 89, 054307 (2014)]. Further, we show that their universal power-law scaling form applies only to some observables in cooling but not to heating. Even in cooling, it is invalid either when an appropriate external field is present. However, this finite-time-finite-size scaling calls for caution in application of FTS. Detailed scaling behaviors of the FTS and finite-size scaling, along with their crossover, are explicitly demonstrated, with the dynamic critical exponent z being estimated for two- and three-dimensional Ising models under the usual Metropolis dynamics. These values of z are found to give rise to better data collapses than the extant values do in most cases but take on different values in heating and cooling in both two- and three-dimensional spaces.

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  • Received 24 July 2014
  • Revised 3 October 2014

DOI:https://doi.org/10.1103/PhysRevB.90.134108

©2014 American Physical Society

Authors & Affiliations

Yingyi Huang, Shuai Yin, Baoquan Feng, and Fan Zhong*

  • State Key Laboratory of Optoelectronic Materials and Technologies, School of Physics and Engineering, Sun Yat-sen University, Guangzhou 510275, People's Republic of China

  • *Corresponding author: stszf@mail.sysu.edu.cn

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Issue

Vol. 90, Iss. 13 — 1 October 2014

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