Fig. 3. Loschmidt echo.

(A) Time evolution of the Loschmidt echo L(t) for different transverse field strengths. (B) Earliest minimum point of L(t) during its dynamics, ${\mathrm{L}}_{\text{min}}^{(1)}$, as a function of h^x/2π. It is shown that ${\mathrm{L}}_{\text{min}}^{(1)}$ is close to zero in the DPP, while it becomes relatively large in the DFP. The behavior of ${\mathrm{L}}_{\text{min}}^{(1)}$ versus h^x is similar to that in the LMG model (see the Supplementary Materials). The solid curves in (A) and (B) are the numerical results using Eq. 1 without considering decoherence.