Natural extension of hartree–fock through extremal 1-fermion information: overview and application to the lithium atom

Fermionic natural occupation numbers do not only obey Pauli's exclusion principle but are even stronger restricted by so-called generalized Pauli constraints. Whenever given natural occupation numbers lie on the boundary of the allowed region the corresponding N-fermion quantum state has a significantly simpler structure. We recall the recently proposed natural extension of the Hartree–Fock ansatz based on this structural simplification. This variational ansatz is tested for the lithium atom. Intriguingly, the underlying mathematical structure yields universal geometrical bounds on the correlation energy reconstructed by this ansatz.</p

Natural extension of hartree–fock through extremal 1-fermion information: overview and application to the lithium atom

Fermionic natural occupation numbers do not only obey Pauli's exclusion principle but are even stronger restricted by so-called generalized Pauli constraints. Whenever given natural occupation numbers lie on the boundary of the allowed region the corresponding N-fermion quantum state has a significantly simpler structure. We recall the recently proposed natural extension of the Hartree–Fock ansatz based on this structural simplification. This variational ansatz is tested for the lithium atom. Intriguingly, the underlying mathematical structure yields universal geometrical bounds on the correlation energy reconstructed by this ansatz.</p

Reconstructing quantum states from single-party information

The possible compatibility of density matrices for single-party subsystems is described by linear constraints on their respective spectra. Whenever some of those quantum marginal constraints are saturated, the total quantum state has a specific, simplified structure. We prove that these remarkable global implications of extremal local information are stable; i.e., they hold approximately for spectra close to the boundary of the allowed region. Application of this general result to fermionic quantum systems allows us to characterize natural extensions of the Hartree-Fock ansatz and to quantify their accuracy by resorting to one-particle information, only: The fraction of the correlation energy not recovered by such an ansatz can be estimated from above by a simple geometric quantity in the occupation number picture

Reconstructing quantum states from single-party information

The possible compatibility of density matrices for single-party subsystems is described by linear constraints on their respective spectra. Whenever some of those quantum marginal constraints are saturated, the total quantum state has a specific, simplified structure. We prove that these remarkable global implications of extremal local information are stable; i.e., they hold approximately for spectra close to the boundary of the allowed region. Application of this general result to fermionic quantum systems allows us to characterize natural extensions of the Hartree-Fock ansatz and to quantify their accuracy by resorting to one-particle information, only: The fraction of the correlation energy not recovered by such an ansatz can be estimated from above by a simple geometric quantity in the occupation number picture

Relating correlation measures: The importance of the energy gap

The concept of correlation is central to all approaches that attempt the description of many-body effects in electronic systems. Multipartite correlation is a quantum information theoretical property that is attributed to quantum states independent of the underlying physics. In quantum chemistry, however, the correlation energy (the energy not seized by the Hartree-Fock ansatz) plays a more prominent role. We show that these two different viewpoints on electron correlation are closely related. The key ingredient turns out to be the energy gap within the symmetry-adapted subspace. We then use a few-site Hubbard model and the stretched H2 to illustrate this connection and to show how the corresponding measures of correlation compare