A self-consistent approach to quantum field theory for extended particles

Karim Zantout, Steffen Backes, Aleksandar Razpopov +2 more

In this paper, we present a multiorbital form of the two-particle self-consistent approach (TPSC) where the effective local and static irreducible interaction vertices are determined by means of the dynamical mean-field theory (DMFT). This approach replaces the approximate ansatz equations for the double-occupations $\ensuremath{\langle}{n}_{\ensuremath{\alpha},\ensuremath{\sigma}}^{}{n}_{\ensuremath{\beta},{\ensuremath{\sigma}}^{\ensuremath{'}}}^{}\ensuremath{\rangle}$ by sampling them directly for the same model using DMFT. Compared to the usual Hartree-Fock-like ansatz, this leads to more accurate local vertices in the weakly correlated regime and provides access to stronger correlated systems that were previously out of reach. This approach is extended by replacing the local component of the TPSC self-energy by the DMFT impurity self-energy, which results in an improved self-energy that incorporates strong local correlations but retains a nontrivial momentum dependence. We find that this combination of TPSC and DMFT provides a significant improvement over the multiorbital formulation of TPSC as it allows to determine the components of the spin vertex without artificial symmetry assumptions and opens the possibility to include the transversal particle-hole channel. The new approach is also able to remove unphysical divergences in the charge vertices in TPSC. We find a general trend that lower temperatures can be accessed in the calculation. Benchmarking single-particle quantities, such as the local spectral function with other many-body methods, we find significant improvement in the more strongly correlated regime.

Jonas B. Profe, Jiawei Yan, Karim Zantout +2 more

Extending many-body numerical techniques which are powerful in the context of simple model calculations to the realm of realistic material simulations can be a challenging task. Realistic systems often involve multiple active orbitals, which increases the complexity and numerical cost because of the large local Hilbert space and the large number of interaction terms or sign-changing off-diagonal Green’s functions. The two-particle self-consistent approach (TPSC) is one such many-body numerical technique, for which multi-orbital extensions have proven to be involved due to the substantially more complex structure of the local interaction tensor. In this paper we extend earlier multi-orbital generalizations of TPSC by setting up two different variants of a fully self-consistent theory for TPSC in multi-orbital systems. We first investigate the strengths and limitations of the approach analytically and then benchmark both variants against dynamical mean-field theory (DMFT) and D-TRILEX results. We find that the exact behavior of the system can be faithfully reproduced in the weak-coupling regime, while at stronger couplings the performance of the two TPSC variants strongly depends on details of the system.

T.M. Samols

E. A. Stepanov, Erik G. C. P. van Loon, A. A. Katanin +3 more

We propose an efficient dual boson scheme, which extends the dynamical mean-field theory paradigm to collective excitations in correlated systems. The theory is fully self-consistent both on the one- and on the two-particle level, thus describing the formation of collective modes as well as the renormalization of electronic and bosonic spectra on equal footing. The method employs an effective impurity model comprising both fermionic and bosonic hybridization functions. Only single- and two-electron Green's functions of the reference problem enter the theory, due to the optimal choice of the self-consistency condition for the effective bosonic bath. We show that the theory is naturally described by a dual Luttinger-Ward functional and obeys the relevant conservation laws.

Bent E. Sørensen