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