Abstract
The Kibble--Zurek mechanism captures universality when a system is driven through a continuous phase transition. Here we study the dynamical aspect of quantum phase transitions in the Ising Field Theory where the quantum critical point can be crossed in different directions in the two-dimensional coupling space leading to different scaling laws. Using the Truncated Conformal Space Approach, we investigate the microscopic details of the Kibble--Zurek mechanism in terms of instantaneous eigenstates in a genuinely interacting field theory. For different protocols, we demonstrate dynamical scaling in the non-adiabatic time window and provide analytic and numerical evidence for specific scaling properties of various quantities. In particular, we argue that the higher cumulants of the excess heat exhibit universal scaling in generic interacting models for a slow enough ramp.
Highlights
Technical details concerning the relation of the adiabatic perturbation theory to the E8 model, the scaling limit of the analytic solution of the dynamics on the transverse field Ising chain and the applicability of Truncated Conformal Space Approach (TCSA) to the study of Kibble–Zurek mechanism (KZM) are discussed in the Appendices
The non-equilibrium dynamics of the Ising Field Theory is amenable to an efficient numerical non-perturbative treatment based on the truncated conformal space approach (TCSA), which we review briefly at the end of the section
Before putting these claims to test by calculating the dynamics of onepoint functions and observing the statistics of excess heat, we investigate the dynamics of energy eigenstates along the ramp in order to sketch an intuitive picture of how the Kibble– Zurek mechanism can be understood at the most fundamental level
Summary
The Kibble–Zurek mechanism (KZM) describes the dynamical aspects of phase transitions and captures the universal features of nonequilibrium dynamics when a system is driven slowly across a continuous phase transition. Apart from its long-standing history to capture equilibrium properties of perturbed conformal field theories [68,69,70,71,72,73,74,75,76,77,78,79,80], recent applications demonstrate that it is capable to describe non-equilibrium dynamics in different models [81,82,83,84,85,86] This approach gives us access to the microscopic data and full statistics of observables so we can investigate the KZM at work at the lowest level, and being nonperturbative and independent of integrability, it allows us to study the dynamics of the interacting field theory. Technical details concerning the relation of the adiabatic perturbation theory to the E8 model, the scaling limit of the analytic solution of the dynamics on the transverse field Ising chain and the applicability of TCSA to the study of KZM are discussed in the Appendices
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