Anomalous self-energy and Fermi surface quasisplitting in the vicinity of a ferromagnetic instability

Abstract

We discuss the low-temperature behavior of the electronic self-energy in the vicinity of a ferromagnetic instability in two dimensions within the two-particle self-consistent approximation, functional renormalization group, and Ward-identity approaches. Although the long-range magnetic order is absent at $T>0$, the self-energy has a non-Fermi-liquid form at low energies $\ensuremath{\mid}\ensuremath{\omega}\ensuremath{\mid}\ensuremath{\lesssim}{\ensuremath{\Delta}}_{0}$ near the Fermi level, where ${\ensuremath{\Delta}}_{0}$ is the ground-state spin splitting. The spectral function at temperatures $T\ensuremath{\lesssim}{\ensuremath{\Delta}}_{0}$ has a two-peak structure with finite spectral weight at the Fermi level. The simultaneous inclusion of self-energy and vertex corrections shows that the above results remain qualitatively unchanged down to very low temperatures $T⪡{\ensuremath{\Delta}}_{0}$. It is argued that this form of the spectral functions implies the quasisplitting of the Fermi surface in the paramagnetic phase in the presence of strong ferromagnetic fluctuations.