Collective and single-particle excitations in a Hubbard antiferromagnet

The spectrum of spin-wave and single-particle excitations is studied in a half-filled-band Hubbard antiferromagnet for interaction strength values in the intermediate and weak-coupling regimes. The spin-wave-energy scale, which goes essentially as t2/U in the strong- and intermediate-coupling regimes, exhibits a crossover and goes down with decreasing interaction strength in the weak-coupling regime. This crossover is found to occur at U/t=3.26, and it demarcates the Heisenberg behavior in the strong- and intermediate-coupling regimes from the spin-density-wave behavior in the weak-coupling regime. The spin-wave-energy scale gets compressed by the charge gap in the weak-coupling regime, and consequently the spin-wave branch, which approaches the single-particle excitation band quite closely, never actually merges into it