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) U ( D ) of spin
U(2) 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 D = 3 -level identical atoms, and we propose the rank of the corresponding reduced density matrix as a discrete order parameter.
Originally introduced in nuclear physics as a numerical laboratory to test different many-body approximation methods, the Lipkin-Meshkov-Glick (LMG) model has received much attention as a simple enough but non-trivial model with many interesting features for areas of physics beyond the nuclear one. In this contribution we look at the LMG model as a particular example of an SU (1,1) Richardson-Gaudin model. The characteristics of the model are analyzed in terms of the behavior of the spectral-parameters or pairons which determine both eigenvalues and eigenfunctions of the model Hamiltonian. The problem of finding these pairons is mathematically equivalent to obtain the equilibrium positions of a set of electric charges moving in a two dimensional space. The electrostatic problems for the different regions of the model parameter space are discussed and linked to the different energy density of states already identified in the LMG spectrum.
The gauge-invariant periodic quantization method is applied to time-dependent states with definite parities in the Lipkin-Meshkov-Glick model. It is shown that the resulting discrete energy spectrum is free of discontinuity and predicts the correct number of states for all interaction strengths. It offers therefore a qualitative improvement over the gauge-invariant periodic quantized time-dependent Hartree-Fock states of this model.NUCLEAR STRUCTURE Time-dependent description of many-body bound states, gauge-invariant periodic quantization method, Lipkin-Meshkov-Glick model, good-parity time-dependent states.