Collective excitations in a doped antiferromagnet

We develop a systematic procedure for studying a doped antiferromagnet in the intermediate-coupling regime. Starting with the Hartree-Fock (HF) solution to the Hubbard model in the half-filled-band case, we obtain the spin-wave spectrum and find that in the strong-coupling limit the spin-wave mode is identical to that obtained from the corresponding spin-(1/2 Heisenberg model. We self-consistently evaluate the one-loop correction to the sublattice magnetization due to spin-wave excitations and in the U/t→∞ limit find that the sublattice magnetization is reduced to 0.6, i.e., to 60% of its HF or saturation value. As a first step toward applying this systematic procedure to a doped antiferromagnetic, we numerically study in detail the HF ground state with few holes, which become self-consistently trapped by the self-induced spin polarization, resulting in the spin-bag ground state. We find that for U/t<20 the transverse terms in the HF Hamiltonian iterate toward zero. We examine the nature of collective excitations in the spin-bag ground state in a 10×10 lattice system for U/t=5, which is representative of the intermediate-coupling regime. We explicitly show that the spin-bag state admits to a stable Goldstone mode, confirming the local stability of this HF state. We analytically examine the self-consistent HF state, obtained in the rigid-band approximation, of a system with finite hole density. We find that, although self-consistent, this HF state is unstable with respect to collective excitations toward the formation of a two-dimensional incommensurate structure with a wave vector proportional to the linear hole density.