How can we describe the formation of order in critical systems? If we tune the control parameters such that the system crosses the critical point, the answer is given by the Kibble-Zurek mechanism (KZM) [1] that predicts universal dependence of observables on the rate of change of the control parameter. In recent years, the focus on quantum critical points [2] demonstrated the validity of the KZM in an extended set of systems. Our work [3] explores the KZM 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 KZM 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.

 

[1] T. W. B. Kibble, Topology of cosmic domains and strings, J. Phys. A: Math. Gen. 9, 1387 (1976); W. H. Zurek, Cosmological experiments in superfluid helium?, Nature 317, 505 (1985).

[2] J. Dziarmaga, Dynamics of a quantum phase transition and relaxation to a steady state, Adv. Phys. 59, 1063 (2010).

[3] K. Hódsági, M. Kormos, Kibble–Zurek mechanism in the Ising Field Theory, SciPost Phys. 9, 055 (2020).