Spin-fermion vertex from exact diagonalization of Hubbard clusters

Abstract

Antiferromagnetic spin fluctuations are a prime suspect for the superconducting glue in cuprates and nickelates. The minimal model reproducing the main physics of these systems is the single-orbital Hubbard model. Diagramatically, the scattering of electrons with these spin fluctuations can be described via a three-point propagator, where the coupling between these two quasiparticles - the propagator with amputated legs - is the Hedin vertex in the magnetic channel, or spin-fermion vertex. It has previously been shown that this coupling shows a rich dependence on fermionic momentum, notably a divergence close to half filling at the antinode. Exact diagonalization calculations for finite clusters in this work reproduce this momentum dependence. Furthermore, the known power law relation from DCA results between the Hedin vertex and the self-energy is also observed. Finally, a physical interpretation of the Hedin vertices' pole at the antinode, due to its established equivalence to the derivative of the self-energy w.r.t to an applied magnetic field is discussed for the 4x4 cluster.