The Anderson lattice model is used to explain the principal features of the heavy fermion compound UGe 2 by means of the generalized Gutzwiller approach (the statistically consistent Gutzwiller approximation method). This microscopic approach successfully reproduces the magnetic and electronic properties of this material, in qualitative agreement with experimental findings from magnetization measurements, neutron scattering, and de Haas-van Alphen oscillations. Most importantly, it explains the appearance, sequence, character, and evolution in an applied magnetic field of the observed in UGe 2 ferromagnetic and paramagnetic phases as an effect of a competition between the f -f electron Coulomb interaction energy and f -conduction electron hybridization.

We provide a microscopic description of the magnetic properties of UGe2 and in particular, of its both classical and quantum critical behavior. Namely, we account for all the critical points: the critical ending point (CEP) at the metamagnetic phase transition, the tricritical point, and the quantum critical end point at the ferromagnetic to paramagnetic phase transition. Their position agrees quantitatively with experiment. Additionally, we predict that the metamagnetic CEP can be traced down to zero temperature and becomes quantum critical point by a small decrease of both the total electron concentration and the external pressure. The system properties are then determined by the quantum critical fluctuations appearing near the instability point of the Fermi surface topology.Introduction. Attempts to determine the quantum critical behavior and the corresponding critical points (QCPs) have attracted much attention due to the unique phenomena with singular physical properties associated with them as temperature T → 0 and other parameters (pressure p, applied field H, or electron concentration n) are varied [1][2][3]. Additionally, in the canonical case-the heavy fermion systems-unconventional superconductivity often appears near those QCPs making the quantum critical fluctuations the primary pairing inducing factor. Also, the classical critical points (CCPs) and their evolution towards QCP provide the testing ground for study of detailed quantitative behavior of different systems [4,5].

We discuss the coexistence of antiferromagnetism and d-wave superconductivity within the socalled statistically-consistent Gutzwiller approximation (SGA) applied to the t-J-U model. In this approach, the averages calculated in a self-consistent manner coincide with those determined variationally. Such consistency is not guaranteed within the standard renormalized mean field theory. With the help of SGA, we show that for the typical value J t = 1 3, coexistence of antiferromagnetism (AF) and superconductivity (SC) appears only for U t > 10.6 and in a very narrow range of doping (δ ≲ 0.006) in the vicinity of the Mott insulating state, in contrast to some previous reports. In the coexistent AF+SC phase, a staggered spin-triplet component of the superconducting gap appears also naturally; its value is very small.