Stability of ferromagnetism within the time-dependent Gutzwiller approximation for the Hubbard model

We study the problem of itinerant ferromagnetism (FM) in one-, two- and infinite-dimensional Hubbard models. Our investigations are based on the time-dependent Gutzwiller approximation (TDGA) which allows for the derivation of a generalized 'GA Stoner criterion' for the instability towards ferromagnetic, but also antiferromagnetic and incommensurate magnetic order. After having established magnetic phase boundaries we investigate the stability of FM by including the effect of transverse fluctuations.We also compute the spin-wave velocity in the ferromagnetic phase and compare our results with other approaches like HF + RPA Stoner theory. Our investigations reveal that even in the fully polarized ferromagnetic phase the TDGA yields a renormalized excitation spectrum with respect to Stoner theory although the double occupancy vanishes in this case.