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

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$\text{}_{2}$Cu$\text{}_{3}$O$\text{}_{4}$Cl$\text{}_{2}$. 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.