Quantum Kibble-Zurek physics in the presence of spatially correlated dissipation

We study how the universal properties of quantum quenches across critical points are modified by a weak coupling to a thermal bath, focusing on the paradigmatic case of the transverse field Ising model. Beyond the standard quench-induced Kibble-Zurek defect production in the absence of the bath, the bath contributes extra thermal defects. We show that spatial correlations in the noise produced by the bath can play a crucial role: one obtains quantitatively different scaling regimes depending on whether the correlation length of the noise is smaller or larger than the Kibble-Zurek length associated with the quench speed, and the thermal length set by the temperature. For the case of spatially correlated bath noise, additional thermal defect generation is restricted to a window that is both quantum critical and excluded from the nonequilibrium regime surrounding the critical point. We map the dissipative quench problem to a set of effectively independent dissipative Landau-Zener problems. Using this mapping along with both analytic and numerical calculations allows us to find the scaling of the excess defect density produced in the quench, and it suggests a generic picture for such dissipative quenches.

Figure 1

Quench trajectories for two temperatures $T_1$ and $T_2$ at a fixed quench rate. At $T_1$, far from the QCP, the spectral gap $\mathrm{\Delta }$ is too large for thermal excitations to be created. Thermal defect generation thus turns on only once the trajectory enters the quantum critical regime $k_{B}T>\mathrm{\Delta }$. It is, however, suppressed again once the system enters the nonequilibrium regime near the QCP, where the intrinsic relaxational rate is slower than the quench rate. The thick yellow dashed line indicates the portion of the quench where thermal defects are produced. For low temperature ($T_2$), the entire quantum critical regime is subsumed within the nonequilibrium regime near the QCP, and hence there is no appreciable thermal defect generation.

Figure 2

Total excitation density $n_{\mathrm{tot}}(v;\gamma ,T)$ vs quench speed $v$ for various temperatures, ${\omega }_c\gg J$, and a system-bath coupling $\gamma =1.3\times {10}^{-6}$. The red full line shows $n_{\mathrm{KZ}}\left(v\right)$, i.e., the excitation density for $\gamma =0$.

Figure 3

Excess thermal defect density associated with the quench, as a function of scaled temperature, for three different quench velocities $v$. For $\sqrt{v}\lesssim T\lesssim J$, the data follow $n_{\mathrm{th}}\propto T^3/v$ in line with the scaling form given in Eq. (7) (orange solid line). Inset: plot of momentum-resolved thermal defect density $P_{\mathrm{th}}(k,v;\gamma ,T)$ for quench velocity $v=1.4\times {10}^{-3}{\text{J}}^2$ and three temperatures.