Orbital Models for Many-Electron Systems

S. Fraga, Gulzari L. Malli, L. H. Thomas

Dmitry S. Golubev, Reza G. Shirazi, Vladimir V. Rybkin +3 more

We propose an approximate mapping of a molecular Hamiltonian to a Hamiltonian of qubits, which allows for high accuracy quantum chemistry calculations of vertical excitation energies of some molecules. The mapping is based on separating of a very small active space of only two orbitals and on modeling the electronic excitations in the remaining orbitals by a set of qubits or, equivalently, by a set of oscillators. This approach is inspired by the Random Phase Approximation (RPA), in which the excitations of electron gas are described by bosonic degrees of freedom. As a result, the Hamiltonian of the molecule is reduced to that of a system-bath model. The "system" part of the Hamiltonian describes the two molecular orbitals -- the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) -- which are populated by two electrons. Two qubits are sufficient to encode the Hamiltonian of such a system. The "bath" consists of oscillators or, equivalently, of two level systems with each of them corresponding to an electron excitation from a doubly occupied orbital below the Fermi level to an empty orbital above the Fermi level. We hope that this mapping can inspire new approaches and algorithms aimed at calculating excitation energies of molecules on near term quantum computers.

Raúl Quintero-Monsebaiz, Ion Mitxelena, Mauricio Rodríguez‐Mayorga +2 more

Natural orbital functional theory is considered for systems with one or more unpaired electrons. An extension of the Piris natural orbital functional (PNOF) based on electron pairing approach is presented, specifically, we extend the independent pair model, PNOF5, and the interactive pair model PNOF7 to describe spin-uncompensated systems. An explicit form for the two-electron cumulant of high-spin cases is only taken into account, so that singly occupied orbitals with the same spin are solely considered. The rest of the electron pairs with opposite spins remain paired. The reconstructed two-particle reduced density matrix fulfills certain N-representability necessary conditions, as well as guarantees the conservation of the total spin. The theory is applied to model systems with strong non-dynamic (static) electron correlation, namely, the one-dimensional Hubbard model with periodic boundary conditions and hydrogen rings. For the latter, PNOF7 compares well with exact diagonalization results so the model presented here is able to provide a correct description of the strong-correlation effects.

Eugene S. Kryachko, Eduardo V. Ludeña

Anatoliy F. Zhuravlyov

Large number of actual heavy-fermionic alloys display non-Fermi liquid behavior [l]. Recent achievements in the description of 1D models give the possibility to indicate some mechanisms of forming special properties of fermionic systems. Usual parameters of these models are Coulomb, orbital, and spin interaction. An 1D integrable model of the Hubbard's chain of the electrons with the model orbital interaction is presented. Exact solutions were obtained for different scattering channels of the electrons, namely the spin and orbital one. The preferable channel of the scattering was determined by means of numerical calculations and comparison of the energy levels of each scattering channel. The dependence of the scattering matrix on the parameters of Coulomb, orbital, and spin interactions gives the possibility to present the properties of the considered system in different ranges of these parameters and to determine the values of parameters which correspond to the electron coupling.