Excited-state quantum phase transitions in many-body systems with infinite-range interaction: Localization, dynamics, and bifurcation

TL;DR

This paper explores excited-state quantum phase transitions in many-body systems with infinite-range interactions, analyzing their detection through Hamiltonian structure, eigenstate localization, bifurcation, and dynamics, using the Lipkin-Meshkov-Glick model.

Contribution

It introduces methods to detect ESQPTs via Hamiltonian analysis, eigenstate localization, and dynamics in systems with infinite-range interactions, exemplified by the LMG model.

Findings

ESQPTs cause local divergences in the density of states.

Detection methods include Hamiltonian structure and eigenstate localization.

Dynamics show similarities between LMG and XX models.

Abstract

Excited state quantum phase transitions (ESQPTs) are generalizations of quantum phase transitions (QPTs) to excited levels. They are associated with local divergences in the density of states. Here, we investigate how the presence of an ESQPT can be detected from the analysis of the structure of the Hamiltonian matrix, the level of localization of the eigenstates, the onset of bifurcation, and the speed of the system evolution. Our findings are illustrated for a Hamiltonian with infinite-range Ising interaction in a transverse field. This is a version of the Lipkin-Meshkov-Glick (LMG) model and the limiting case of the one-dimensional spin-1/2 system with tunable interactions realized with ion traps. From our studies for the dynamics, we uncover similarities between the LMG and the noninteracting XX models.