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While the diagonalization of a quadratic bosonic form can always be done using a Bogolyubov transformation, the practical implementation for systems with a large number of different bosons is a tedious analytical task. Here we use the coupled cluster method to exactly diagonalise such complicated quadratic forms. This yields to a straightforward algorithm which can easily be implemented using computer algebra even for a large number of different bosons. We apply this method on a Heisenberg system with two interpenetrating square lattice antiferromagnets, which is a model for the quasi-2D antiferromagnet Ba 2 Cu3 O 4 Cl2 . Using a four-magnon spin wave approximation we get a complicated Hamiltonian with four different bosons, which is treated with coupled cluster method. Results are presented for magnetic ground state correlations. PACS numbers: 75.50.Ee, 75.30.Ds, 31.15.Dv, 42.50.Lc

Diagonalization of a Bosonic Quadratic Form Using CCM: Application on a System with Two Interpenetrating Square Lattice Antiferromagnets