Excited-state quantum phase transitions and chaos in a three-level Lipkin model

TL;DR

This paper explores excited-state quantum phase transitions in a three-level Lipkin model, analyzing how chaos influences spectral structures and establishing a framework for studying ESQPTs in complex, chaotic quantum systems.

Contribution

It introduces a comprehensive static analysis framework for ESQPTs in a three-level Lipkin model, incorporating chaos-sensitive measures and spectral diagnostics.

Findings

Chaos-sensitive measures effectively identify chaotic regions.

Spectral structures are strongly influenced by chaos and multiple separatrices.

The framework aids future dynamical studies of ESQPTs in complex systems.

Abstract

Excited-state quantum phase transitions (ESQPTs) have been extensively studied in two-level models, but their characterization remains challenging in systems displaying mixed regular and chaotic dynamics. In this work, we investigate ESQPTs within the three-level Lipkin-Meshkov-Glick model, where an enlarged Hilbert space and multiple separatrices give rise to rich spectral structures strongly influenced by chaos. To investigate the different dynamical regions, we have calculated Poincar\'e sections and Peres lattices. In addition, by combining chaos-sensitive measures with standard ESQPT diagnostics, we provide a static analysis of ESQPT signatures in this model and establish a robust framework for future studies of its dynamical behavior. The degree of chaos and the Kullback-Leibler divergence are found to be very effective chaos-sensitive measures, which are complementary to ESQPT diagnostics such as the mean field limit and the participation ratio. Hence we provide a standard framework to work with ESQPTs in chaotic three-level systems.