Exploring Coupled Cluster Green's function as a method for treating system and environment in Green's function embedding methods

Abstract

Within the self-energy embedding theory (SEET) framework, we study coupled cluster Green's function (GFCC) method in two different contexts: as a method to treat either the system or environment present in the embedding construction. Our study reveals that when GFCC is used to treat the environment we do not see improvement in total energies in comparison to the coupled cluster method itself. To rationalize this puzzling result, we analyze the performance of GFCC as an impurity solver with a series of transition metal oxides. These studies shed light on strength and weaknesses of such a solver and demonstrate that such a solver gives very accurate results when the size of the impurity is small. We investigate if it is possible to achieve a systematic accuracy of the embedding solution when we increase the size of the impurity problem. We found that in such a case, the performance of the solver worsens, both in terms of finding the ground state solution of the impurity problem as well as the self-energies produced. We concluded that increasing the rank of GFCC solver is necessary to be able to enlarge impurity problems and achieve a reliable accuracy. We also have shown that natural orbitals from weakly correlated perturbative methods are better suited than symmetrized atomic orbitals (SAO) when the total energy of the system is the target quantity.

Interaction expansion inchworm Monte Carlo solver for lattice and impurity models

“…'Diagrammatic' Monte Carlo (DiagMC) methods, i.e. Monte Carlo methods that sample diagrammatic perturbation theories [12,13], have proven to be effective solution methods for quantum impurity models, along with exact diagonalization (ED) [14,15], renormalization group [16,17], tensor network [18][19][20], and several quantum chemistry approaches [21][22][23][24]. In particular, continuous-time methods (CT-QMC) [25] are currently the gold standard for the solution of impurity problems generated by most embedding approaches.…”