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TT: Fachverband Tiefe Temperaturen

TT 86: Correlated Electrons: Method Development

TT 86.10: Vortrag

Freitag, 22. März 2024, 12:00–12:15, H 3007

Analytic results for the two-particle vertex in the atomic limit of the Hubbard model — •Stefan Rohshap, Markus Wallerberger, Karsten Held, and Anna Kauch — Institute of Solid State Physics, TU Wien, 1040 Vienna, Austria

Much of the physics of strongly correlated electrons contained in the Hubbard model can already be understood by studying its atomic limit. Although the exact analytical expressions for the atomic one- and two-particle Green’s functions are easily obtained, this is not the case for the two-particle irreducible vertex functions. These are of particular interest due to the presence of vertex divergences that are also present in the full Hubbard model [1]. Analytic expressions for irreducible vertices were so far only found for the half-filled single-orbital atom, by means of a sophisticated matrix inversion procedure that to our knowledge cannot be generalized [2].

In this contribution, we will present a new generalized technique based on a pole expansion method that allows the derivation of a set of analytic algebraic equations for determining the irreducible vertex also in the multiorbital case at arbitrary filling. We will show that this system of algebraic equations can be solved by choosing a suitable ansatz and exemplify it on the case of the single-band Hubbard atom. Moreover, we will present a new method for identifying vertex divergences based on the calculation of the determinant of the generalized susceptibility.

[1] T. Schäfer et al., Phys. Rev. B 94 (2016) 235108

[2] P. Thunström et al., Phys. Rev. B 98 (2018) 235107

Keywords: Hubbard model in the atomic limit; pole expansion method; Bethe-Salpeter equation; irreducible vertex function and vertex divergences; determinant method