In this work, we focus on the critical dynamics of the one-dimensional quasiperiodic $p$-wave-paired Aubry-André-Harper model, which exhibits a transition point between the gapped critical and the gapless localized phases. First, we disclose that the dynamical exponent features two distinct plateaus in the gapless localized phase. Besides the plateau with dynamical exponent $z=1.388$ near the transition point, there is a second one with $z=1$ away from the transition point. Then we demonstrate that these two plateaus intrinsically affect the critical dynamics with moderate quench rate by employing both one-way and round-trip quench protocols. In the one-way quench protocol, we clarify that the Kibble-Zurek (KZ) regime consists of two subregimes with different KZ exponents, which is a direct consequence of the two-plateau structure of the dynamical exponent. We also diagnose the KZ, presaturated, and saturated regimes by varying the quench rate from slow to fast limits while, in the round-trip quench protocol, we observe the defect density exhibits a clear oscillatory interference pattern with a steady period within the KZ regime. More intriguingly, a bottleneck appears in the pattern, which reflects the turning of the two KZ subregimes.

Close

PrevNext

View figure in article

• Critical exponents
• Dynamical phase transitions
• Quantum criticality
• Quantum quench
• 1-dimensional systems
• Disordered systems