Cumulant approach to weakly doped antiferromagnets

We present an approach to static and dynamical properties of holes and spins in weakly doped antiferromagnets in two dimensions. The calculations are based on a recently introduced cumulant approach to ground endash state properties of correlated electronic systems. The present method allows us to evaluate hole and spin-wave dispersion relations by considering hole or spin excitations of the ground state. Usually, these dispersions are found from time-dependent correlation functions. To demonstrate the ability of the approach we first derive the dispersion relation for the lowest single hole excitation at half-filling. However, the main purpose of this paper is to focus on the mutual influence of mobile holes and spin waves in the weakly doped system. It is shown that low-energy spin excitations strongly admix to the ground state. The coupling of spin waves and holes leads to a strong suppression of the staggered magnetization which cannot be explained by a simple rigid-band picture for the hole quasiparticles. Also the experimentally observed doping dependence of the spin-wave excitation energies can be understood within our formalism. copyright 1996 The American Physical Society