Spin-rotationally-symmetric path-integral formulation of a generalizedN-orbital Hubbard model

Abstract

A spin-rotationally-symmetric path-integral formulation with a vector order parameter is presented for a generalized scrN-orbital Hubbard model which yields the correct Hartree-Fock result in the saddle-point approximation, and also the spin-wave mode representing transverse Gaussian fluctuations. A systematic expansion of the action in powers of inverse scrN, wherein spin-rotational symmetry and hence the Goldstone mode are preserved order by order, is developed, and the first order O(1/scrN) quantum corrections to the ground-state energy and sublattice magnetization obtained. Setting scrN=1 yields a quantitatively correct description of the antiferromagnetic state of the one-orbital Hubbard model at half-filling.