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

TL;DR

This paper investigates how the Lipkin-Meshkov-Glick model's dynamics after a sudden quench reveal critical behavior, with distinct signatures in free energy, irreversible work, and spectral functions across the quantum phase transition.

Contribution

It demonstrates that post-quench dynamics and spectral properties can serve as indicators of quantum criticality in the Lipkin-Meshkov-Glick model.

Findings

Different dynamics observed when quenching through the critical point.

Free energy and irreversible work rates differ between phases.

Spectral functions reveal fundamental excitations governing post-quench behavior.

Abstract

We examine the dynamics after a sudden quench in the magnetic field of the Lipkin-Meshkov-Glick model. Starting from the groundstate 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 post-quenched system, further highlighting the qualitative differences between the dynamics in the two phases.