Figure 1

(a) Spin-spin correlation function for the TFI chain for a ramp to the QCP ($t=0$), showing scaling collapse for a wide range of slow ramp rates. The inset shows correlation functions prior to scaling. (b) Scaled correlation length and (c) correlation function as a function of scaled time (b),(c) and distance (c) during the ramp. The KZ correlation length deviates from equilibrium near $t{v}^{1/2}=-2.5$ and remains finite at the QCP and beyond. We define the correlation length as $\xi v^{1/2}=\sqrt{{\int }_0^{\infty }g(\chi ){\chi }^{2}d\chi /{\int }_0^{\infty }g(\chi )d\chi }$, where $\chi =x{v}^{1/2}$. All data in this figure are in the KZ thermodynamic limit, $L{v}^{1/2}\gg 1$ (see text).Reuse & Permissions

Figure 2

Results of tMPS simulations for ramping the experimentally realizable MITP model (see text), which is illustrated in the inset to (a). The data show scaling collapse of MITP (colored dots) to the scaling limit of the TFI chain (black lines) as a function of scaled time $\tau =t{v}^{1/2}$ (a), scaled system size $\Lambda =L{v}^{1/2}$ (a),(b), and scaled length $x/L$ (b),(c) [21]. We have checked that data for $\Lambda =30$ is near the $\Lambda =\infty$ limit for the TFI model (not shown), although finite-size effects can still be seen in (c). The arrow in the inset to (c) indicates the maximum ramp duration that produces athermal negative correlations in a twelve-site bosonic chain (data from Ref.[11]; see the Supplemental Material [27] for details).Reuse & Permissions