Two-orbital quantum discord in fermion systems

TL;DR

This paper derives a simple formula for quantum discord between two orbitals in fermion systems, highlighting how natural orbitals influence quantum correlations and analyzing specific models to illustrate these effects.

Contribution

It introduces a straightforward method to compute quantum discord in fermion systems and explores the role of natural orbitals in quantum correlations, especially under particle number symmetry.

Findings

Quantum discord vanishes between natural orbital pairs when pairing tensor is zero.

Quantum correlations depend on the orbital basis chosen, especially in non-natural bases.

Analysis of Lipkin-Meshkov-Glick and Agassi models illustrates the theoretical findings.

Abstract

A simple expression to compute the quantum discord between two orbitals in fermion systems is derived using the parity superselection rule. As the correlation between orbitals depends on the basis chosen, we discuss a special orbital basis, the natural one. We show that quantum correlations between natural orbital pairs disappear when the pairing tensor is zero, i.e. the particle number symmetry is preserved. The Hartree-Fock orbitals within a Slater determinant state, a Hartree-Fock-Bogoliubov quasiparticle orbitals in a quasiparticle vacuum, or the ground state of a Hamiltonian with particle symmetry and their corresponding natural orbitals are some relevant examples of natural basis and their corresponding states. Since natural orbitals have that special property, we seek for the quantum discord in non-natural orbital basis. We analyze our findings in the context of the Lipkin-Meshkov-Glick and Agassi models.