The Lipkin-Meshkov-Glick model: 'quasi-local' quantum criticality in nuclear physics

TL;DR

This paper investigates the Lipkin-Meshkov-Glick model in nuclear physics, revealing a new crossover temperature and quantum critical phenomena analogous to condensed matter systems, highlighting 'quasi-local' quantum criticality.

Contribution

It introduces the concept of a crossover temperature T*(V,W) in the LMG model, linking nuclear physics to condensed matter quantum criticality and identifying quantum order-by-disorder effects.

Findings

Identification of a new crossover temperature T*(V,W).

Logarithmic vanishing of T* near the quantum phase transition.

Observation of quantum order-by-disorder phenomena.

Abstract

Motivated by recent work on local quantum criticality in condensed matter systems, we study the Lipkin-Meshkov-Glick (LMG) model of nuclear physics as a simple model of a kind of 'quasi-local' quantum criticality. We identify a new crossover temperature, T*(V,W), between linear and nonlinear dynamics, which is analogous to the crossover between the renormalized classical and quantum critical regimes in the condensed-matter case. This temperature T* typically vanishes logarithmically as the quantum phase transition is approached, except near the quantum tricritical point where it becomes linear. We also note a further analogy with condensed-matter quantum criticality: the LMG model exhibits quantum order-by-disorder phenomena, of the type often associated with phase reconstruction near quantum critical points.