Coupled Cluster as an Impurity Solver for Green’s Function Embedding Methods

Abstract

We investigate the performance of Green's function coupled cluster singles and doubles (CCSD) method as a solver for Green's function embedding methods. To develop an efficient CC solver, we construct the one-particle Green's function from the coupled cluster (CC) wave function based on a non-hermitian Lanczos algorithm. The major advantage of this method is that its scaling does not depend on the number of frequency points. We have tested the applicability of the CC Green's function solver in the weakly to strongly correlated regimes by employing it for a half-filled 1D Hubbard model projected onto a single site impurity problem and a half-filled 2D Hubbard model projected onto a 4-site impurity problem. For the 1D Hubbard model, for all interaction strengths, we observe an excellent agreement with the full configuration interaction (FCI) technique, both for the self-energy and spectral function. For the 2D Hubbard, we have employed an open-shell version of the current implementation and observed some discrepancies from FCI in the strongly correlated regime. Finally, on an example of a small ammonia cluster, we analyze the performance of the Green's function CCSD solver within the self-energy embedding theory (SEET) with Hartee-Fock (HF) and Green's function second order (GF2) for the treatment of the environment.

Efficient Formulation of Ab Initio Quantum Embedding in Periodic Systems: Dynamical Mean-Field Theory

“…We recently studied the coupled-cluster Green's function (CCGF) approximation as an impurity solver in DMFT 33 (see also Ref. 60 ) and showed that it performed well for small impurity clusters in Hubbard models. Here, we further explore its capabilities in the ab initio setting.…”

Ab initio Calculations in Atoms, Molecules, and Solids, Treating Spin-Orbit Coupling and Electron Interaction on Equal Footing

“…Single-determinant trial wave functions are often sufficient for many AFQMC calculations; however, sometimes multideterminant wave functions are needed for reaching chemical accuracy (for example in transition metal containing systems) [11,68,69]. Efficient implementations of multideterminant trial wavefunctions with a sublinear scaling in the number of determinants have been developed [70][71][72].…”

Diagrammatic Monte Carlo method for impurity models with general interactions and hybridizations

“…Since the Green's function G, self-energy , as well as the total electronic energy E = E 0 + E V can all be derived from the scattering matrix M using Eqs. 20, (32), (33), it is sufficient to only keep track of the amputated diagrams A c (V ) and obtain all other observables as derived quantities. Table I summarizes some of these measurements.…”

“…A wide range of such methods exist. Hamiltonian-based methods, such as exact diagonalization (ED) [25][26][27][28][29] and its variants [30], configuration-interactions [31] cluster theory [32,33], solve the impurity problem by mapping the impurity problem onto a system with a local Hamiltonian and a finite number of auxiliary "bath" states chosen to fit the time-dependent hybridization function. The methods are limited to a relatively small set of strongly interacting sites or breakdown at moderate correlation strength.…”