Ferromagnetic Quantum critical behavior in three-dimensional Hubbard model with transverse anisotropy

One-band Hubbard model with transverse anisotropy is considered at density of electrons $n=0.4$. It is shown that when the anisotropy is appropriately chosen, the ground state is ferromagnetic with magnetic order perpendicular to the anisotropy. The increasing of the ratio $\frac tU$, where $t$ is the hopping parameter and $U$ is the Coulomb repulsion, decreases the Curie temperature, and the system arrives at the quantum critical point $(T_C=0)$. The result is obtained introducing Schwinger bosons and slave Fermions representation of the electron operators. Integrating out the spin-singlet Fermi fields an effective Heisenberg model with ferromagnetic exchange constant is obtained for vectors which identifies the local orientation of the spin of the itinerant electrons. The amplitude of the spin vectors is an effective spin of the itinerant electrons accounting for the fact that some sites, in the ground state, are doubly occupied or empty. Owing to the anisotropy, the magnon fluctuations drive the system to quantum criticality and when the effective spin is critically small these fluctuations suppress the magnetic order.