Dynamics following a linear ramps in the $O(N)$ model: dynamical transition and statistics of excitations

TL;DR

This paper investigates the non-thermal dynamical phase transition in the $O(N)$ model under linear ramp protocols, revealing a robust critical behavior and crossover phenomena between sudden quench and equilibrium quantum critical points.

Contribution

It demonstrates the persistence of dynamical phase transitions under linear ramps and analyzes the crossover between different critical regimes in the $O(N)$ model.

Findings

Dynamical phase transition exists for all ramp durations.

Statistics of excitations show robust critical behavior.

Crossover in equal time correlation functions indicates anomalous coarsening.

Abstract

Non-thermal dynamical critical behavior can arise in isolated quantum systems brought out of equilibirum by a change in time of their parameters. While this phenomenon has been studied in a variety of systems in the case of a sudden quench, here we consider its sensitivity to a change of protocol by considering the experimentally relevant case of a linear ramp in time. Focusing on the $O(N)$ model in the large $N$ limit, we show that a dynamical phase transition is always present for all ramp durations and discuss the resulting crossover between the sudden quench transition and one dominated by the equilibrium quantum critical point. We show that the critical behavior of the statistics of the excitations, signaling the non-thermal nature of the transition are robust against changing protocol. An intriguing crossover in the equal time correlation function, related to an anomalous coarsening is also discussed.