Correlation energy and quantum correlations in a solvable model
Javier Faba, Vicente Martín, L. M. Robledo
Abstract
Typically in many-body systems the correlation energy, which is defined as the difference between the \nexact ground-state energy and the mean-field solution, has been a measure of the system’s total correlations. \nHowever, under the quantum information context, it is possible to define some quantities in terms of the system’s \nconstituents that measure the classical and quantum correlations, such as the entanglement entropy, mutual \ninformation, quantum discord, one-body entropy, etc. In this work we apply concepts of quantum information in \nfermionic systems in order to study traditional correlation measures (the relative correlation energy). Concretely, \nwe analyze the two- and three-level Lipkin models, which are exactly solvable (but nontrivial) models commonly \nused in the context of the many-body problem. We conclude that the correlation energy is not a good estimator \nof the total correlation of the system, and information theoretic measures should be considered