Fig. 3
(Color plot) The transition probability \(p_{k}\) following the quench from the initial value of transverse field \(h_{i}=-10\) to the various values of quench field end \(h_{f}\) for various sweep velocities. (a) for \(J_{3}=1/4\) and \(h_{f}=-0.5\) where the ramped quench crosses a single Ising like quantum critical point \(h^{(1)}_{c}=-3/4\), (b) for \(J_{3}=1\) and \(h_{f}=-0.5\) where the ramped quench crosses single quantum critical points \(h^{(a)}_{c}=-1\), (c) for \(J_{3}=1/4\) and \(h_{f}=1.5\) where the quench crosses two Ising like quantum critical points \(h^{(1)}_{c}=-3/4\), and \(h^{(1)}_{c}=5/4\) (d) for \(J_{3}=1\) and \(h_{f}=1.5\) where the ramped quench crosses two quantum critical points \(h^{(a)}_{c}=-1\) and \(h^{(1)}_{c}=0\), (e) for \(J_{3}=1\) and \(h_{f}=10\), where the ramped quench crosses three quantum critical points \(h^{(a)}_{c}=-1\), \(h^{(1)}_{c}=0\), and \(h^{(2)}_{c}=2\). (f) The dynamical phase diagram of the model in the \((J_{3}; v)\) plane in the absence of the noise for a quench from \(h_i=-10\) to \(h_{f}=1.5\). The diagram is divided into three regions. The horizontal yellow dashed-dotted line represents \(J_3=1/2\) and \(J_3=5/2\). The blue solid line separates two regions where the system shows SCM and ThCMs. The red solid line shows the boundary between regions characterized by TwCMs and those with no-DQPTs. The blurred gray dashed-dotted curves represent the boundaries obtained from LZ transition formula.
