Scaling and Universality at Noisy Quench Dynamical Quantum Phase Transitions

TL;DR

This paper investigates how noise affects dynamical quantum phase transitions in the extended XY model, revealing scaling laws, critical mode behavior, and universality under noisy conditions.

Contribution

It introduces the first analysis of noise effects on DQPTs in the extended XY model, uncovering new scaling relations and critical mode phenomena.

Findings

Critical sweep velocity decreases with noise strength.

Number of critical modes increases when noise and sweep velocity are comparable.

Scaling of dynamical free energy remains universal under noise.

Abstract

Dynamical quantum phase transitions (DQPTs) have been studied in the extended XY model under both noiseless and noisy linear driven staggered field cases. In the time-independent staggered field case, the model exhibits a single critical point where the transition occurs from the spin-liquid phase to the antiferromagnetic phase. In the noiseless ramp case, unlike the transverse field XY model where DQPT always occurs for a quench crossing the single critical point, there is a critical sweep velocity above which the kinks corresponding to a DQPT are completely removed. Furthermore, in this case there are only two critical modes whose excitation probability is one-half. In the presence of a Gaussian white noise, we find that this critical sweep velocity decreases by increasing the noise strength, and scales linearly with the square of the noise intensity. A surprising result occurs when the noise intensity and sweep velocity are about the same order of magnitude, the number of critical modes is significantly increased, signalling a region with multiple critical modes. Furthermore, our findings indicate that the scaling of the dynamical free energy near the DQPTs time is the same for both noiseless and noisy ramp quenches.