Report on scipost_202007_00061v1

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 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 a genuinely interacting field theory. We demonstrate dynamical scaling in the non-adiabatic time window and provide analytic and numerical evidence for specific scaling properties of various quantities, including higher cumulants of the excess heat. Contents 1 Introduction 2 2 Model and methods 4 2.1 The Kibble-Zurek mechanism 4 2.2 KZM in the Ising Field Theory 6 2.3 Adiabatic Perturbation Theory 9 2.3.1 Application to the Ising Field Theory 11 2.4 Truncated Conformal Space Approach 13 3 Work statistics and overlaps 14 3.1 Ramps along the free fermion line 15 3.1.1 The paramagnetic-ferromagnetic (PF) direction 15 3.1.2 The ferromagnetic-paramagnetic (FP) direction 17 3.2 Ramps along the E 8 line 19 3.3 Probability of adiabaticity 20 3.4 Ramps ending at the critical point 21 4 Dynamical scaling in the non-adiabatic regime 22 4.1 Free fermion line 23 4.2 Ramps along the E 8 axis 24 5 Cumulants of work 25 5.1 ECP protocol: ramps ending at the critical point 26 5.2 TCP protocol: ramps crossing the critical point 28 6 Conclusions 29 A Application of the adiabatic perturbation theory to the E 8 model 31 A.1 One-particle states 31 A.2 Two-particle states 32 B Ramp dynamics in the free fermion field theory 35 C TCSA: detailed description, extrapolation 36 C.1 Conventions and applying truncation 36 C.2 Extrapolation details 37 References 41