Optimized adiabatic-impulse protocol preserving Kibble-Zurek scaling with attenuated anti-Kibble-Zurek behavior

TL;DR

This paper introduces an optimized adiabatic-impulse protocol that shortens quantum phase transition crossing times while maintaining Kibble-Zurek scaling, and reduces noise-induced defects in quantum systems.

Contribution

The authors develop an optimized adiabatic-impulse protocol that preserves Kibble-Zurek scaling and mitigates anti-Kibble-Zurek behavior under noise, with applications to the transverse Ising chain.

Findings

Sublinear power-law dependence of evolution time on quench time

Significant attenuation of noise-induced defects using the OAI protocol

Universal power-law scaling of optimal quench time with noise strength

Abstract

We propose an optimized adiabatic-impulse (OAI) protocol that substantially reduces the evolution time for crossing a quantum phase transition while preserving Kibble-Zurek (KZ) scaling. Near criticality, the control parameter is ramped linearly across the critical point at a rate characterized by a quench time $\tau_Q$. Away from criticality, the evolution remains adiabatic and is tuned close to the threshold of adiabatic breakdown, as quantified by an adiabatic coefficient $\zeta$ that scales as $\tau_Q^\alpha$. As a consequence, the total evolution time exhibits a sublinear power-law dependence on $\tau_Q$, and the conventional linear quench is recovered in the limit $\alpha\rightarrow\infty$. We apply the OAI protocol to the transverse Ising chain and numerically determine the minimal $\zeta$ required for KZ scaling. We further investigate the nonequilibrium dynamics in the presence of a noisy field that can induce anti-Kibble-Zurek (AKZ) behavior. Within the OAI protocol, noise-induced defects is significantly attenuated due to the shorter evolution time. The optimal quench time at which the defect density is minimized obeys an altered universal power-law scaling with the noise strength. Finally, we generalize the OAI protocol to the nonlinear quenches and numerically demonstrate a marked reduction in noise-induced defects.