Abstract
We consider the annealing dynamics of a one-dimensional Ising ferromagnet induced by a temperature quench in finite time. In the limit of slow cooling, the asymptotic two-point correlator is analytically found under Glauber dynamics, and the distribution of the number of kinks in the final state is shown to be consistent with a Poissonian distribution. The mean kink number, the variance, and the third centered moment take the same value and obey a universal power-law scaling with the quench time in which the temperature is varied. The universal power-law scaling of cumulants is corroborated by numerical simulations based on Glauber dynamics for moderate cooling times away from the asymptotic limit, when the kink-number distribution takes a binomial form. We analyze the relation of these results to physics beyond the Kibble-Zurek mechanism for critical dynamics, using the kink number distribution to assess adiabaticity and its breakdown. We consider linear, nonlinear, and exponential cooling schedules, among which the latter provides the most efficient shortcuts to cooling in a given quench time. The non-thermal behavior of the final state is established by considering the trace norm distance to a canonical Gibbs state.
Highlights
Nonequilibrium phenomena occupy a prominent role at the frontiers of physics, where few and highly valuable paradigms are able to provide a description making use of equilibrium properties
We focus on the last, as it provides a framework to analyze the course of a phase transition and the breakdown of adiabatic dynamics leading to the formation of topological defects
We focus on the distribution of kinks in the nonequilibrium state resulting from cooling the Ising ferromagnet in a finite time
Summary
Nonequilibrium phenomena occupy a prominent role at the frontiers of physics, where few and highly valuable paradigms are able to provide a description making use of equilibrium properties. The mean number of defects but as well the variance, third centered moment, and any cumulant of the kink-number distribution of higher order have been shown to scale following a universal power-law with the quench time [41,42,43] This prediction has been experimentally explored using a trapped ion for the quantum simulation of critical dynamics in momentum space [43]. The first three cumulants of the kink-number distribution are explicitly shown to be equal and described by a universal power law with the quench time, indicating that the slow cooling of an Ising ferromagnet under the Glauber dynamics yields a Poissonian kink-number distribution The relevance of these findings to finite annealing times is verified by numerical simulations, in which we consider three different families of cooling schedules: linear, nonlinear, and exponential quenches. Additional details of explicit calculations and numerics can be found in the Appendixes
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
