Ab Initio Full Cell GW+DMFT for Correlated Materials

Abstract

Quantitative prediction of electronic properties in correlated materials requires simulations without empirical truncations and parameters. We present a method to achieve this goal through a new ab initio formulation of dynamical mean-field theory (DMFT). Instead of using small impurities defined in a low-energy subspace, which require complicated downfolded interactions which are often approximated, we describe a full cell GW+DMFT approach, where the impurities comprise all atoms in a unit cell or supercell of the crystal. Our formulation results in large impurity problems, which we treat here using an efficient coupled-cluster impurity solver that works on the real-frequency axis, combined with a one-shot G 0 W 0 treatment of long-range interactions. We apply our full cell approach to bulk Si and two antiferromagnetic correlated insulators, NiO and -Fe 2 O 3 , with impurities containing up to 10 atoms and 124 orbitals. We find that spectral properties, magnetic moments, and two-particle spin correlation functions are obtained in good agreement with experiments. In addition, in the metal oxides, the balanced treatment of correlations involving all orbitals in the cell leads to new insights into the orbital character around the insulating gap.

Dependence of DFT+DMFT results on the construction of the correlated orbitals

“…On the theoretical side, our work highlights the importance of the development of methods [75,76] which treat more of the orbitals as correlated and include more of the matrix elements of the Coulomb interaction. While not all of these calculations are yet in a position to treat the strong correlation problem, comparison even in a more weakly correlated limit will provide insight.…”

Testing the GFCCSD impurity solver on real materials within the self-energy embedding theory framework

“…Recent studies [12,13] have also utilized GFCCSD as the impurity solver in the DMFT-type embedding scheme where realistic impurity problems are constructed based on HF [12] and G 0 W 0 [13]. In these studies, the strength of GFCCSD is manifested by its ability to deal with an impurity problems which encompasses all the orbitals inside a unit cell.…”

“…At present embedding methods such as dynamical mean field theory (DMFT) [1], self-energy embedding theory (SEET) [2][3][4][5], or density matrix embedding theory (DMET) [6,7] for treating realistic problems reached a significant sophistication and can be routinely applied to perform calculations for systems with relatively complicated electronic structure such as transition metal oxides (e.g. NiO, MnO solids) [5,[8][9][10][11][12][13] or oxide perovskites (e.g. SrVO 3 , SrMnO 3 , and many others) [14][15][16][17][18][19][20].…”

“…Recently, the coupled cluster (CC) method [23] at the level of singles and doubles (CCSD) was adapted to work as a solver in conjunction with DMFT [12,13,25] and SEET [24] schemes. We will call this solver a Green's function coupled cluster (GFCC) solver.…”

“…While the CC method originated in the nuclear physics community, early on it was adapted by quantum chemists where it was primarily used to treat weakly correlated molecular systems. The early tests of the CC solver were performed on the impurities coming from the 1D and 2D Hubbard models [24,25], small molecular systems [24] and limited solids [13]. These tests demonstrated that the GFCCSD solver can be used in weakly to moderately strongly correlated situations.…”