Mean-field theory for vacancies in a quantum antiferromagnet

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Abstract
The vacancies in a quantum antiferromagnet have dipolar interactions mediated by antiferromagnetic (AF) spin waves. An effective Hamiltonian incorporating this effect is studied within a mean-field approximation. The ground state is found to be an s- or d-wave superconductor. In the strong-coupling regime the superconductivity coexists with the incommensurate spiral AF order. The analysis is limited to the regime where the AF correlation length is larger than the distance between vacancies.