Examples for ClassicalLMG

Exponential growth of the FOTOC using the TWA

In Ref. [12], it was shown that the fidelity out-of-time order correlator (FOTOC) corresponding the the unstable fixed point $(Q,P)=(0,0)$ at the excited-state quantum phase transition of the Lipkin-Meshkov-Glick (LMG) model grows eponentially, even though it is a regular system. In this example we calculate such quantity using the Truncated Wigner Approximation (TWA)

using DickeModel.TWA, DickeModel.ClassicalLMG
using Plots

fixed_point = ClassicalLMG.Point(Q=0, P=0)

systemLMG = ClassicalLMGSystem(Ω=1, ξ=-1)
j = 500
W = coherent_Wigner_SU2(fixed_point, j =j)
ts=0:0.1:50
FOTOC= sum.(
        variance(systemLMG,
            observable = [:Q,:P],
            N = 5000,
            ts = ts,
            distribution = W)
    )

plot(ts,FOTOC,
    yscale=:log10,
    xlabel="time",
    ylabel="FOTOC",
    key=false)