Defect formation beyond Kibble-Zurek mechanism and holography

TL;DR

This paper develops a theoretical framework for early-time evolution and defect formation after a smooth quench across a second order phase transition, revealing a new non-adiabatic period and a defect rate smaller than Kibble-Zurek predictions.

Contribution

It introduces a novel formalism for the early dynamics of phase transitions, predicting a different defect formation rate and breakdown criteria for Kibble-Zurek scaling.

Findings

Identifies a non-adiabatic coarsening period post-transition.

Predicts defect formation rate smaller than Kibble-Zurek.

Validates the theory with holographic superfluid simulations.

Abstract

We study the dynamic after a smooth quench across a continuous transition from the disordered phase to the ordered phase. Based on scaling ideas, linear response and the spectrum of unstable modes, we develop a theoretical framework, valid for any second order phase transition, for the early-time evolution of the condensate in the broken phase. Our analysis unveils a novel period of non-adiabatic evolution after the system passes through the phase transition, where a parametrically large amount of coarsening occurs before a well-defined condensate forms. Our formalism predicts a rate of defect formation parametrically smaller than the Kibble-Zurek prediction and yields a criterion for the break-down of Kibble-Zurek scaling for sufficiently fast quenches. We numerically test our formalism for a thermal quench in a 2 + 1 dimensional holographic superfluid. These findings, of direct relevance in a broad range of fields including cold atom, condensed matter, statistical mechanism and cosmology, are an important step towards a more quantitative understanding of dynamical phase transitions.