Collective excitations in the ferro-and antiferromagnetic states of the two-dimensional repulsive Hubbard model

Abstract

Collective excitations in the antiferromagnetic and ferromagnetic states of the two-dimensional repulsive Hubbard model are investigated both in the phase transition vicinity (Ginsburg-Landau region |T−T_c|≪T_c) and in the low-temperature region T≪T_c using the functional integration method. The spectrum of collective excitation consists of one branch at T>T_c, and another branch (Goldstone branch) arises at T<T_c. The Goldstone branch at T≪T_c in the antiferromagnetic state is calculated including the anisotropic correction term to the linear dispersion law. The value of the nonphonon branch at the zero momentum is equal to the double gap of the fermion energy 2Δ. All the spectrum branches in the ferromagnetic state vanish at zero momentum$\left( {\mathop {\lim }\limits_{k \to 0} E\left( k \right) = 0} \right)$. Bibliography: 6 titles.