Evolution of the spectral function for the AIM

This animation shows the evolution for a simple Anderson impurity model (AIM) for rising hybridization strength from the atomic limit to a strongly coupled system.
The Hamiltonian reads H=-2.0 d^\dagger d + 4.0 d^\dagger_\uparrow d_\uparrow d^\dagger_\downarrow d_\downarrow + \sum_k \varepsilon_k c^\dagger_k c_k + \sum_k V_k (c^\dagger_k d + d^\dagger c_k) with bath energies \varepsilon_k marked in red in the graph (implicit spin summation).

out

The excitation energies of the atomic limit at \varepsilon_d=-2.0 and \varepsilon_d + U=2.0 are marked in green. A nice evolution from the atomic spectrum at small hybridizations with lower and upper Hubbard peaks over some kind of a Kondo resonance at the Fermi energy for intermediate hybridizations (V_k \sim 0.2-0.3) to a fully coupled system with two peaks corresponding to the bonding and anti bonding orbital, one wandering down and one up in energy with increasing hybridization.