An efficient method for strongly correlated electrons in two-dimensions

Abstract

This work deals with the problem of strongly correlated electrons in two-dimensions (2D). We give a reduced density matrix (RDM) based tool through which the ground-state energy is given as a functional of the natural orbitals and their occupation numbers. Specifically, the Piris Natural Orbital Functional 7 (PNOF7) is used for studying the 2D Hubbard model and hydrogen square lattices. The singlet ground-state is studied, as well as the doublet mixed quantum state obtained by extracting an electron from the system. Our method satisfies two-index necessary N-representability conditions of the two-particle RDM (2RDM) and guarantees the conservation of the total spin. We show the ability of PNOF7 to describe strong correlation effects in 2D systems by comparing our results with exact diagonalization, density matrix renormalization group (DMRG), and auxiliaryfield quantum Monte Carlo calculations. PNOF7 overcomes variational 2RDM methods with twoand three-index positivity N-representability conditions, reducing computational cost to mean-field scaling. Consistent results are obtained for small and large systems up to 144 electrons, weak and strong correlation regimes, and many filling situations. Unlike other methods, there is no dependence on dimensionality in the results obtained with PNOF7, and no particular difficulties have been observed to converge PNOF7 away from half-filling. Smooth double occupancy of sites is obtained regardless of the filling. Symmetric dissociation of 2D hydrogen lattices shows that long-range nondynamic correlation drammatically affects electron detachment energies. PNOF7 compares well with DMRG along the dissociation curve.

Density Matrices of Seniority-Zero Geminal Wavefunctions

“…40,41,[118][119][120][121][122][123][124][125][126][127][128][129] Variational APSG is equivalent to the Piris natural orbital functional PNOF5, 130,131 meaning that the APSG 2-RDM is expressible directly in terms of its 1-RDM elements. Recently, the PNOF7 functional [132][133][134][135][136][137] has shown convincing numerical results. In its simplest form PNOF7 is based on closed-shell pairs (generalizations are possible and pointed out in ref 132 ), but the intra-pair and inter-pair interactions are treated separately.…”

Relativistic reduced density matrix functional theory

“…The lack of intersubspace interaction in PNOF5 lead to the later versions of PNOFx functionals (like PNOF7). The PNOF7 functional accounts for the interaction among pairs and has been proven account for the so-called nondynamic correlation energy, but it misses the dynamic one [34,35,103]. In an attempt to account for both types of electron correlation the GNOF functional was recently proposed [106]; it has proven to be capable of accounting for an important part of the so-called dynamic correlation energy.…”

“…RDMFT is emerging as a strong competitor to the widely used density functional theory (DFT) due to the possibility to use fractional occupation numbers, which facilitates the study of electronic systems where the socalled nondynamic correlation effects are enhanced [29][30][31][32][33][34][35]. Indeed, the popular working horse of physicists and chemists (i.e.…”

Benchmarking GNOF against FCI in challenging systems in one, two and three dimensions

“…The use of the first-order RDM (1RDM) Γ to describe the correlated electronic structure leads to a reduction of the computational cost of 2RDM approaches, and do not compromise the accuracy for studying strongly correlated systems [12,13]. In contrast to DFT, the one-electron energy functional is exactly known in terms of Γ, however, we have to settle for making approximations for the reconstruction of the unknown electron-electron interaction energy functional.…”