Correlation energy and quantum correlations in a solvable model

TL;DR

This paper explores the relationship between correlation energy and quantum correlations in solvable fermionic models, using quantum information concepts to provide new insights into many-body systems.

Contribution

It introduces a novel approach applying quantum information measures to analyze correlation energy in exactly solvable Lipkin models.

Findings

Correlation energy relates to quantum correlations in the models.

Quantum information measures provide new insights into many-body correlations.

The Lipkin models serve as a testbed for these concepts.

Abstract

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.