Quantum critical behavior in three-dimensional one-band Hubbard model at half-filling

•Technique of calculation is introduced which permits us to study the magnons’ fluctuations.•Quantum critical point is obtained in the one-band 3D Hubbard model at half-filling.•The present analytical results supplement the numerical ones (see Fig. 7).

A one-band Hubbard model with hopping parameter tt and Coulomb repulsion UU is considered at half-filling. By means of the Schwinger bosons and slave fermions representation of the electron operators and integrating out the spin–singlet Fermi fields an effective Heisenberg model with antiferromagnetic 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. Accounting adequately for the magnon–magnon interaction the Néel temperature is calculated. When the ratio tU is small enough (tU≤0.09) the effective model describes a system of localized electrons. Increasing the ratio increases the density of doubly occupied states which in turn decreases the effective spin and Néel temperature. The phase diagram in the plane of temperature TNU and parameter tU is presented. The quantum critical point (TN=0TN=0) is reached at tU=0.9. The magnons in the paramagnetic phase are studied and the contribution of the magnons’ fluctuations to the heat capacity is calculated. At the Néel temperature the heat capacity has a peak which is suppressed when the system approaches a quantum critical point. It is important to stress that, at half-filling, the ground state, determined by fermions, is antiferromagnetic. The magnon fluctuations drive the system to quantum criticality and when the effective spin is critically small these fluctuations suppress the magnetic order.