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

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 Schrödinger 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.