Cumulant-expansion study of holes in quantum antiferromagnets

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Abstract
The states of a single hole and of two holes in the planar quantum antiferromagnet are studied within the t-J model by performing the cumulant expansion in t/J and in the exchange anisotropy γ. Ground-state energies are calculated up to the n=12 order in t/J and to the m=6 order in γ. It is shown that results, which can be extended to smaller J/t, represent a very helpful supplement to exact diagonalization methods. In particular they yield finite-size corrections to previous results on the dispersion of single-hole states and to the binding energy of two holes, giving also more insight into the origin of binding.