Criticality revealed through quench dynamics in the Lipkin-Meshkov-Glick model

We examine the dynamics after a sudden quench in the magnetic field of the Lipkin-Meshkov-Glick model. Starting from the ground state and by employing the time-dependent fidelity, we see manifestly different dynamics are present if the system is quenched through the critical point. Furthermore, we show that the average work shows no sensitivity to the quantum phase transition; however, the free energy and irreversible work show markedly different rates of change in each phase. Finally, we assess the spectral function showing the fundamental excitations that dictate the dynamics of the postquenched system, further highlighting the qualitative differences between the dynamics in the two phases.