We show that the Gutzwiller variational wave function is surprisingly accurate for the computation of magnetic phase boundaries in the infinite dimensional Hubbard model. This allows us to substantially extend known phase diagrams. For both the half-hypercubic and the hypercubic lattice a large part of the phase diagram is occupied by an incommensurate phase, intermediate between the ferromagnetic and the paramagnetic phase. In case of the hypercubic lattice the three phases join at a new quantum Lifshitz point at which the order parameter is critical and the stiffness vanishes.PACS numbers: 71.10. Fd,75.25.+z,75.30.Kz The Hubbard model was originally introduced to study ferromagnetism in strongly correlated metals [1,2,3]. This phenomenon as prototypically realized in Fe, Co and Ni is one of the oldest phenomena investigated in solid state theory. A related problem is incommensurate spin-density-wave order as manifested in Cr and its alloys [4]. Also various transition metal oxides show incommensurate magnetic phases which are often accompanied by charge order, like cuprates [5], nickelates [6] and manganites [7].Despite decades of investigation not much is known about the magnetic phase diagram of the Hubbard model. The simplest treatments [8,9] partition the zero temperature phase diagram in three regions: antiferromagnetic (AFM) close to n = 1 particles per atom, ferromagnetic (FM) at large interaction and far from n = 1 and paramagnetic (PM) at small interaction and/or close to n = 0, 2. More sophisticated treatments include in addition incommensurate (IC) phases [10,11].Infinite dimensional lattices offer an unique opportunity to study the competition between PM and FM keeping the problem tractable and, at the same time, retaining much of the physics expected in three dimensional lattices [12]. Here we investigate the Hubbard model in the limit of infinite dimension D using the Gutzwiller variational wave function (GWF) [13]. Instabilities of the FM and PM ground state are systematically studied as a function of momentum, doping, and interaction strength using a random-phase-approximation (RPA) like expansion [15,16,17]. In principle the model can be solved exactly in this limit by using dynamical mean-field theory (DMFT) which maps the problem to an impurity problem amenable of numerical solution [12]. Limitations on the numerical algorithm, however, have prevented for an extensive zero temperature investigation of the phase diagram. A study by Uhrig on the stability of the FM phase in an infinite dimensional generalization of the fcc lattice, the so called half-hypercubic (hhc) lattice, is one of the few cases where the T = 0 self-consistent DMFT problem has been solved exactly [14].Here we show, comparing with exact results when available, that the celebrated GWF is surprisingly accurate for the determination of magnetic phase boundaries in infinite dimensional lattices. In addition we significantly extend the computation of the T = 0 magnetic phase diagram to regions in parameter space yet poorly exp...

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 þ 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.

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