Correlation energy and quantum correlations in a solvable model

Typically in many-body systems the correlation energy, which is defined as difference between exact ground state energy and mean-field solution, has been a measure of system's total correlations. However, under quantum information context, it possible to define some quantities terms constituents that classical correlations, such entanglement entropy, mutual information, discord, one-body etc. In this work, we apply concepts fermionic order study traditional measures (the relative energy) from novel approach. Concretely, analyze two three level Lipkin models, are exactly solvable (but non trivial) models very used context problem.