Symmetry and energy spectrum of high-nuclearity spin clusters

A general and efficient procedure is presented, which allows us to reduce the computational efforts for the calculation of the energy levels of high-nuclearity spin clusters. The method consists of block factorizing the Hamiltonian matrix using the invariance of the spin Hamiltonian with regard to interchanges of spin sites. It can be applied to any arbitrary spin Hamiltonian. In order to demonstrate the flexibility in handling different spin Hamiltonian terms and symmetry groups, its application to several model clusters is discussed.