Topological Defects from Quantum Reset Dynamics

Abstract

We analyze mechanisms for universal out-of-equilibrium dynamics near criticality by exploring the effect of randomized quantum resetting (QR) under a finite-time quench across a quantum phase transition. Using the transverse-field Ising chain as a generic model and exploiting its exact solution, QR is found to cause a crossover of the scaling of the topological defect density with the time scale $τ$ of the quench, from Kibble-Zurek to anti-Kibble-Zurek scaling as $τ$ increases. This reflects a competition between non-adiabatic quench-driven excitations and QR, giving rise to local minima of the defect densities at optimal annealing times. These times and the corresponding local minima are shown to scale as universal power laws with the rate of QR. Additional results for the scaling of the mean excess energy suggest that a system driven across a quantum critical point exhibits the same scaling behavior under a linear quench with QR as with uncorrelated noise.

Figures (3)

• Figure 1: (a) Log-log plot of the density of defects $n_r$ generated by a quench with QR from $h_i(0) = 2$ to $h_f(2\tau) = 0$ as a function of the quench time scale $\tau$ for different values of QR rate $r$. (b) Difference $\delta n_r = n_r-n_0$ between the density of generated defects from the quench in (a) with [$n_r$] and without [$n_0$] QR. (c) Data collapse of the curves in panel (b) after rescaling $\delta n_r \rightarrow e^{-\delta_r}\delta n_r$. All data in the figure are obtained from a chain with 1000 sites.
• Figure 2: Scaling of the optimal quantum annealing times $\tau_{\text{opt},r}$ with QR rate $r$. Inset: Scaling of the local minima of defect densities $n_r^{\text{min}}$ with $r$.
• Figure 3: Residual mean energy $Q_r$ after a quench with QR as a function of the time scale $\tau$ of the quench for different values of QR rate $r$.