Towards ab initio Calculations with the Dynamical Vertex Approximation

Abstract

While key effects of the many-body problem-such as Kondo and Mott physics-can be understood in terms of onsite correlations, non-local fluctuations of charge, spin, and pairing amplitudes are at the heart of the most fascinating and unresolved phenomena in condensed matter physics. Here, we review recent progress in diagrammatic extensions to dynamical mean-field theory for ab initio materials calculations. We first recapitulate the quantum field theoretical background behind the two-particle vertex. Next we discuss latest algorithmic advances in quantum Monte Carlo simulations for calculating such two-particle quantities using worm sampling and vertex asymptotics, before giving an introduction to the ab initio dynamical vertex approximation (AbinitioDΓA). Finally, we highlight the potential of AbinitioDΓA by detailing results for the prototypical correlated metal SrVO 3 .

Strong-coupling formula for momentum-dependent susceptibilities in dynamical mean-field theory

“…Regarding the impurity solver, we used hybridization expansion algorithm of the continuous-time quantum Monte Carlo (CTQMC) method 26,27 in the region U/W 1.5. In the strong-coupling regime U/W 1.0, we used the Hubbard-I approximation to obtain a stable solution, avoiding statistical errors (see Appendix A for some remarks).…”

“…The basic idea is presented in Ref. 3, which showed that the antiferromagnetic (AFM) transition temperature covers the paramagnetic Mott transition in the Hubbard model. For early and recent reviews of the method, see Refs.…”

“…The DMFT takes full account of local correlations, which is responsible for formation of a local moment, and therefore offers a good starting point in addressing long-range ordering. Applications of the DMFT have expanded from models to materials by combining first-principles calculations within the density functional theory (DFT+DMFT) 2 .…”

“…On the other hand, the static component χ(q) allows systematic investigations of phase transitions. This method has been applied to various correlated models such as the Hubbard model [3][4][5][6] , the periodic Anderson model 7 , and variants of the Kondo lattice model [8][9][10][11] . It has also been applied to material calculations within the DFT+DMFT framework [12][13][14] .…”

“…This additional process of computing χ(q) becomes particularly harder in multiorbital systems, since the number of susceptibility components increases in proportion to N 4 orb , where N orb is the number of orbitals. Toward realistic susceptibility calculations including full orbitals, efforts have been made to develop an efficient treatment of the BS equation 15 and the vertex part [16][17][18][19][20][21] . Related developments are addressed, for example, in solving the parquet equation 22 and diagrammatic extensions of the DMFT 23,24 .…”