Abstract
Kibble-Zurek theory (KZ) stands out as the most robust theory of defect generation in the dynamics of phase transitions. KZ utilizes the structure of equilibrium states away from the transition point to estimate the excitations due to the transition using adiabatic and impulse approximations. Here we show, the actual nonequilibrium dynamics lead to a qualitatively different scenario from KZ, as far correlations between the defects (rather than their densities) are concerned. For a quantum Ising chain, we show, this gives rise to a Gaussian spatial decay in the domain wall (kinks) correlations, while KZ would predict an exponential fall. We propose a simple but general framework on top of KZ, based on the ``quantum coarsening'' dynamics of local correlators in the supposed impulse regime. We outline how our picture extends to generic interacting situations.
Highlights
The Kibble-Zurek mechanism (KZM) provides arguably the simplest and most robust theory that captures the dynamics of a continuous quantum phase transition (QPT) both in the classical [1,2,3,4,5] and quantum [6,7,8,9,10,11,12,13,14] realms
(5) While our focus lies on extending the theory of dynamics at QPT beyond Kibble-Zurek theory (KZ), we emphasize that our picture naturally connects with KZ; in particular, length and timescales appearing in the novel defect correlations exhibit KZ scaling
Following the provision of a nontrivial initial state generated by the ramp, we are led to a novel Generalized Gibbs’ Ensemble (GGE), apparently naturally accessible only via such a route
Summary
The Kibble-Zurek mechanism (KZM) provides arguably the simplest and most robust theory that captures the dynamics of a continuous quantum phase transition (QPT) both in the classical [1,2,3,4,5] and quantum [6,7,8,9,10,11,12,13,14] realms. Where a parameter (temperature/coupling) is ramped across the transition point at a finite rate, it predicts the universal scaling of the resulting defect density with the ramp rate (Kibble-Zurek (KZ) scaling laws). This relies on the socalled adiabatic-impulse (AI) approximation, which approximates the dynamics into two qualitatively different regimes. (5) While our focus lies on extending the theory of dynamics at QPT beyond KZ, we emphasize that our picture naturally connects with KZ; in particular, length and timescales appearing in the novel defect correlations exhibit KZ scaling.
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