Perturbation and mean field theory

Corentin Bertrand, Michel Ferrero, Olivier Parcollet

We show how to use diagrammatic techniques to compute the weak-coupling perturbation series of the self-consistent solution to a dynamical mean field theory (DMFT) problem. This approach constitutes an alternative to using diagrammatic techniques directly as an impurity solver. It allows one to bypass the need of multiple perturbative series resummations within the DMFT self-consistency loop. It can be applied at or out of equilibrium, with any diagrammatic formalism, such as real times, imaginary times, or Matsubara frequencies formalisms. As a proof of principle, we illustrate our method with the half-filled Hubbard model on the Bethe lattice in the DMFT approximation, using quantum quasi Monte Carlo (QQMC) to obtain the impurity perturbation series on the real time axis.

Dieter Vollhardt, Krzysztof Byczuk, Marcus Kollar

V. I. Tokar, R. Monnier

A technique allowing for a perturbative treatment of nonlocal corrections to the single-site dynamical mean-field theory (DMFT) in finite dimensions is developed. It is based on the observation that in the case of strong electron correlation the one-electron Green's function is strongly spatially damped so that its intersite matrix elements may be considered as small perturbations. Because the non-local corrections are at least quadratic in these matrix elements, DMFT in such cases may be a very accurate approximation in dimensions d = 1-3. This observation provides a rigorous justification for the application of DMFT to physical systems. Furthermore, the technique allows for a systematic evaluation of the nonlocal corrections. This is illustrated with the calculation of the magnetic short range order parameter for nearest neighbor spins in the half filled Hubbard model on the square lattice in its insulating phase which exhibits an excellent agreement with the results of a recent cluster approach.As a second example we study the lowest order correction to the DMFT self-energy and its influence on the local density of states.

Ryota Mizuno, Masayuki Ochi, Kazuhiko Kuroki

Although several impurity solvers in the dynamical mean field theory (DMFT) have been proposed, especially in multiband systems, there are practical difficulties arising from a trade-off between numerical costs and reliability. In this study, we reinterpret the iterative perturbation theory (IPT) as an approximation which captures the strong correlation effects by mimicking the particular frequency structures of the exact full vertex, and extend it such that it can have efficiency and reliability simultaneously by modifying IPT vertex using the parquet equations. We apply this method to several models to evaluate their validity. We confirm that our method shows good agreements with the numerically exact continuous-time quantum Monte Carlo method in the single-site DMFT calculation.