Kibble-Zurek scaling in quantum speed limits for shortcuts to adiabaticity

Abstract

Geometric quantum speed limits quantify the tradeoff between the rate at which quantum states can change and the resources that are expended during the evolution. Counterdiabatic driving is a unique tool from shortcuts to adiabaticity to speed up quantum dynamics while completely suppressing nonequilibrium excitations. We show that the quantum speed limit for counterdiabatically driven systems undergoing quantum phase transitions fully encodes the Kibble-Zurek mechanism by correctly predicting the transition from adiabatic to impulse regimes. Our findings are demonstrated for three scenarios, namely the transverse field Ising model, the Landau-Zener model, and the Lipkin-Meshkov-Glick model.