Information diagrams in the study of entanglement in symmetric multi-quDit systems and applications to quantum phase transitions in Lipkin-Meshkov-Glick D-level atom models

TL;DR

This paper employs information diagrams and generalized coherent states to analyze entanglement and quantum phase transitions in symmetric multi-quDit systems, specifically applying these methods to Lipkin-Meshkov-Glick models of D=3-level atoms.

Contribution

It introduces the use of information measures and the rank of reduced density matrices as tools to study entanglement and phase transitions in multi-level atomic systems.

Findings

Correlation measures characterize quantum phase transitions.

Rank of reduced density matrix acts as a discrete order parameter.

Analysis extends to D-level atom models.

Abstract

In this paper we pursue the use of information measures (in particular, information diagrams) for the study of entanglement in symmetric multi-quDit systems. We use generalizations to U(D) of spin U(2) coherent states and their adaptation to parity (multicomponent Schr\"odinger cats) and we analyse one- and two-quDit reduced density matrices. We use these correlation measures to characterize quantum phase transitions occurring in Lipkin-Meshkov-Glick models of D=3-level identical atoms and we propose the rank of the corresponding reduced density matrix as a discrete order parameter.