Dynamical Vertex Approximation for the attractive Hubbard model

by Lorenzo Del Re, TU Wien

Tuesday 12 Jun 2018, 15:00 → 16:00 Europe/Berlin

Room 222 (Jungiusstr. 9)

In this seminar, I will present an extension of the formalism of the Dynamical Vertex Approximation (D$\Gamma$A) [1], a diagrammatic approach including many-body correlations beyond the Dynamical Mean-Field Theory [2], to treat the case of attractive on-site interactions. I will first introduce the method from a theoretical point of view and briefly review some of the already published results for the repulsive case [3-5]. Then, I will derive the equations for the attractive case proving the validity of the derivation by showing, both analytically and numerically, that the results obtained in the particle-hole symmetric case fully preserve the exact mapping between the attractive and the repulsive models [6]. Furthermore, I will show an application of the extended algorithm to the attractive Hubbard model in three dimensions, for different fillings and interaction values. Specifically, I will focus on the parameter region in the proximity of the second-order transition to the superconducting and charge-density wave phase, respectively, and show (i) their phase-diagrams, (ii) their critical behavior, as well as (iii) the effects of the strong non-local correlations on the single-particle properties. [1] A. Toschi et al., Phys. Rev. B 75, 045118 (2007) [2] A. Geroges et al., Rev. Mod. Phys. 68, 13 (1996) [3] G. Rohrigner et al., Phys. Rev. Lett. 107, 256402 (2011) [4] T. Schäfer et al., Phys. Rev. B 91, 125109 (2015) [5] G. Rohrigner et al., arXiv:1705.00024 (2017) [6] L. Del Re, M. Capone, A. Toschi, arXiv: 1805.05194 (2018)