Correlation energy and quantum correlations in a solvable model

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). Concretely, we analyze the two- and three-level Lipkin models, which are exactly solvable (but nontrivial) models commonly used in the context of the many-body problem. We conclude that the correlation energy is not a good estimator of the total correlation of the system, and information theoretic measures should be considere