SCALING BEHAVIOR OF THE GROUND-STATE FIDELITY IN THE LIPKIN–MESHKOV–GLICK MODEL

In this paper, we study the scaling behavior of the ground-state logarithmic fidelity in the Lipkin-Meshkov-Glick (LMG) model. We find that the logarithmic fidelity shows a different scaling behavior in different phases of the model. It is an extensive quantity in the model's symmetry-broken phase while it behaves intensively in the polarized phase. Moreover, we also find that the logarithmic fidelity shows a singular behavior around the vicinity of the critical point and the critical exponent of the correlation length is also obtained numerically.