Strong-coupling functional renormalization group: Nagaoka ferromagnetism and non-Fermi liquid physics in the Hubbard model at U = ∞

We develop an extension of the fermionic functional renormalization group for systems where strong correlations give rise to projected Hilbert spaces. We use our method to calculate the phase diagram and the electronic spectral function of the Hubbard model at infinite on-site repulsion where many-body states involving doubly occupied lattice sites are eliminated from the physical Hilbert space. For a square lattice with nearest-neighbor hopping we find that the ground state evolves from a paramagnetic Fermi liquid at low densities via a state with antiferromagnetic stripe order at intermediate densities to an extended Nagaoka ferromagnet at high densities. In the strongly correlated magnetic phases, the electrons form an incoherent non-Fermi liquid. Both at high and low densities, the volume of the Fermi surface is not constrained by Luttinger's theorem.