Excited-State Quantum Phase Transitions in the Anharmonic Lipkin-Meshkov-Glick Model: Dynamical Aspects

TL;DR

This paper investigates the dynamical effects of a newly identified excited-state quantum phase transition (ESQPT) caused by anharmonicity in the Lipkin-Meshkov-Glick model, revealing its impact on quantum quench dynamics and related observables.

Contribution

It introduces a quantum quench analysis of the anharmonic LMG model, highlighting the dynamical consequences of the second ESQPT on various quantum evolution measures.

Findings

The new ESQPT influences the survival probability after a quantum quench.

It affects the local density of states and Loschmidt echoes.

The dynamical effects are similar to those of the standard ESQPT.

Abstract

The standard Lipkin-Meshkov-Glick (LMG) model undergoes a second-order ground-state quantum phase transition (QPT) and an excited-state quantum phase transition (ESQPT). The inclusion of an anharmonic term in the LMG Hamiltonian gives rise to a second ESQPT that alters the static properties of the model [Phys. Rev. E 106, 044125 (2022)]. In the present work, the dynamical implications associated to this new ESQPT are analyzed. For that purpose, a quantum quench protocol is defined on the system Hamiltonian that takes an initial state, usually the ground state, into a complex excited state that evolves on time. The impact of the new ESQPT on the time evolution of the survival probability and the local density of states after the quantum quench, as well as on the Loschmidt echoes and the microcanonical out-of-time-order correlator (OTOC) are discussed. The anharmonity-induced ESQPT, despite having a different physical origin, has dynamical consequences similar to those observed in the ESQPT already present in the standard LMG model.