Sonic horizons and causality in the phase transition dynamics
Abstract
A system gradually driven through a symmetrybreaking phase transition is subject to the KibbleZurek mechanism (KZM). As a consequence of the critical slowing down, its state cannot follow local equilibrium, and its evolution becomes nonadiabatic near the critical point. In the simplest approximation, that stage can be regarded as "impulse" where the state of the system remains unchanged. It leads to the correct KZM scaling laws. However, such "freezeout" might suggest that the coherence length of the nascent order parameter remains unchanged as the critical region is traversed. By contrast, the original causalitybased discussion emphasized the role of the {\it sonic horizon}: domains of the broken symmetry phase can expand with a velocity limited by the speed of the relevant sound. This effect was demonstrated in the quantum Ising chain where the dynamical exponent $z=1$ and quasiparticles excited by the transition have a fixed speed of sound. To elucidate the role of the sonic horizon, in this paper we study two systems with $z>1$ where the speed of sound is no longer fixed, and the fastest excited quasiparticles set the size of the sonic horizon. Their effective speed decays with the increasing transition time. In the extreme case, the dynamical exponent $z$ can diverge such as in the Griffiths region of the random Ising chain where localization of excited quasiparticles freezes the growth of the correlation range when the critical region is traversed. Of particular interest is an example with $z<1$  the longrange extended Ising chain, where there is no upper limit to the velocity of excited quasiparticles with small momenta. Initially, the powerlaw tail of the correlation function grows adiabatically, but in the nonadiabatic stage it lags behind the adiabatic evolutionin accord with a generalized LiebRobinson bound.
 Publication:

arXiv eprints
 Pub Date:
 December 2019
 arXiv:
 arXiv:1912.02815
 Bibcode:
 2019arXiv191202815S
 Keywords:

 Quantum Physics;
 Condensed Matter  Quantum Gases
 EPrint:
 17 pages