Dynamical vertex approximation for the two-dimensional Hubbard model

TL;DR

This paper applies the dynamical vertex approximation (DΓA), a diagrammatic extension of DMFT, to study the phase diagram and gap formation in the two-dimensional Hubbard model, revealing a gradual crossover and a fully gapped Fermi surface at low temperatures.

Contribution

It demonstrates the use of DΓA for analyzing the 2D Hubbard model, providing insights into phase transitions and gap evolution beyond traditional methods.

Findings

Identification of two transition lines in the phase diagram.

Gradual crossover between different gap regimes.

At low temperatures, the entire Fermi surface is gapped.

Abstract

Recently, diagrammatic extensions of dynamical mean field theory (DMFT) have been proposed for including short- and long-range correlations beyond DMFT on an equal footing. We employ one of these, the dynamical vertex approximation (D$\Gamma$A), and study the two-dimensional Hubbard model on a square lattice. We define two transition lines in the phase diagram which correspond, respectively, to the opening of the gap in the nodal direction and throughout the Fermi surface. Our self-energy data show that the evolution between the two regimes occurs in a gradual way (crossover) and also that at low enough temperatures the whole Fermi surface is always gapped. Furthermore, we present a comparison of our D$\Gamma$A calculations at a parameter set where data obtained by other techniques are available.