Space of initial conditions and universality in nonequilibrium quantum dynamics

TL;DR

This paper investigates how initial conditions influence the nonequilibrium quantum dynamics of one-dimensional ferromagnets, revealing universal behavior inside the light cone and phase transitions akin to classical wetting phenomena.

Contribution

It provides an analytical framework for understanding the role of initial conditions in quantum quenches and identifies universal space-time behavior across different models.

Findings

Universal form of local operator expectation values inside the light cone.

Dependence of the global limit shape on initial conditions.

Interaction tuning induces a nonequilibrium quantum phase transition similar to classical wetting.

Abstract

We study analytically the role of initial conditions in nonequilibrium quantum dynamics considering the one-dimensional ferromagnets in the regime of spontaneously broken symmetry. We analyze the expectation value of local operators for the infinite-dimensional space of initial conditions of domain wall type, generally intended as initial conditions spatially interpolating between two different ground states. At large times the unitary time evolution takes place inside a light cone produced by the spatial inhomogeneity of the initial condition. In the innermost part of the light cone the form of the space-time dependence is universal, in the sense that it is specified by data of the equilibrium universality class. The global limit shape in the variable $x/t$ changes with the initial condition. In systems with more than two ground states the tuning of an interaction parameter can induce a transition which is the nonequilibrium quantum analog of the interfacial wetting transition occurring in classical systems at equilibrium. We illustrate the general results through the examples of the Ising, Potts and Ashkin-Teller chains.