Dresden 2014 – wissenschaftliches Programm
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TT: Fachverband Tiefe Temperaturen
TT 79: Correlated Electrons - Poster Session
TT 79.61: Poster
Mittwoch, 2. April 2014, 15:00–19:00, P2
Algebraic-diagrammatic algorithm for the high-order perturbation expansion of the Green’s function in the Mott-Hubbard insulator in high dimensions — Eva Kalinowski1, Walter Apel2,3, •Martin Paech3,1, and Eric Jeckelmann3 — 1Academy of Computer Science and Management, Bielsko-Biała, Poland — 2Physikalisch-Technische Bundesanstalt, Braunschweig, Germany — 3Leibniz Universität, Hannover, Germany
One of the open problems in the theory of Mott-Hubbard insulators is the shape of the Hubbard bands in the single-particle density of states (DOS). In particular, for the Hubbard model on a Bethe lattice in the limit of an infinite coordination number, dynamical mean-field theory (DMFT) calculations reveal some unexplained sharp structures at the low-energy edges of the Hubbard bands in both the Mott insulating phase and the metallic phase in the critical region. Previous analytical expansions (up to second order for the Hubbard model and up to third order by solving the DMFT self-consistency equation) cannot fully explain the observed structures.
We show that the calculation of the DOS can also be formulated in a form, which is amenable to an algebraic-diagrammatic approach. We prove this procedure for the case of the Falicov-Kimball model and determine manually the DOS and the gap up to the fourth order for the Hubbard model. Additionally, we outline the generalization of an algorithm [1], which is well established for the ground-state energy and related critical properties up to the 15th order, for the computation of higher orders of the Green’s function and the gap.
PRB 85, 045105