Communication: The description of strong correlation within self-consistent Green's function second-order perturbation theory

Abstract

We report an implementation of self-consistent Green's function many-body theory within a second-order approximation (GF2) for application with molecular systems. This is done by iterative solution of the Dyson equation expressed in matrix form in an atomic orbital basis, where the Green's function and self-energy are built on the imaginary frequency and imaginary time domain, respectively, and fast Fourier transform is used to efficiently transform these quantities as needed. We apply this method to several archetypical examples of strong correlation, such as a H32 finite lattice that displays a highly multireference electronic ground state even at equilibrium lattice spacing. In all cases, GF2 gives a physically meaningful description of the metal to insulator transition in these systems, without resorting to spin-symmetry breaking. Our results show that self-consistent Green's function many-body theory offers a viable route to describing strong correlations while remaining within a computationally tractable single-particle formalism.

Efficient Temperature-Dependent Green’s Function Methods for Realistic Systems: Using Cubic Spline Interpolation to Approximate Matsubara Green’s Functions

“…GF2 is a perturbative many-body Green's function method that has many attractive properties. It is as accurate as Møller-Plesset perturbation theory (MP2) [67] for weakly correlated systems but, unlike many methods suitable for weakly correlated systems such as MP2 or CCSD [68], it is reasonably well behaved for strongly correlated systems [52]. GF2 has both small fractional charge and fractional spin errors [69], affordable computational scaling O(N τ n 5 ) and can be carried out selfconsistently, making it reference independent.…”

“…In the left panel of Fig. 3, we plotted several of the largest elements of the imaginary part of the Matsubara Green's function for the H 2 CO molecule calculated using the second-order Green's function theory (GF2) [51,52,62] with TZ(Dunning) basis set. In the right panel of Fig.…”

“…It was shown in ref 45 that the coefficients of high-frequency expansion in a non-orthogonal orbital basis for Hamiltonians with full Coulomb interaction are given by In a typical calculation, see Fig. 1, the self-energy Σ is evaluated either on the Matsubara frequency or imaginary time grid by a variety of solvers ranging from quantum Monte Carlo methods [7,[46][47][48] to perturbative [49][50][51][52][53][54] and configuration interaction type of methods [55,56]. In the next step, a Green's function is calculated by means of the Dyson equation…”

Communication: Configuration interaction combined with spin-projection for strongly correlated molecular electronic structures

“…This system has been studied by other authors as a model system that represents a metal-insulator transition as the lattice parameter a increases. 16,38 When a → ∞, its electronic structure exhibits very complicated spin-entanglement, and its complete description requires an active space of (12e, 12o), which is nothing but FCI for a minimal STO-3G basis and requires 853 776 determinants. As shown in Figure 3, while many sophisticated spin-restricted and unrestricted methods break down for this system, both ECISD and ECISD+Q offer a balanced description between dynamic and static correlations.…”

“…[5][6][7][8][9][10][11][12][13][14][15][16] Among them, projected Hartree-Fock (PHF) stands on symmetrybreaking and restoration in the mean-field picture and delivers static correlations efficiently. 12,17 Scuseria et al have extended PHF to describe the residual dynamic correlations by sequentially updating and adding PHF wave functions based on approximate excited PHF states.…”