Operator matrices generation: Combinatorial structures in finite spin models Original Research Article

Finite spin models, applicable in investigation of mesoscopic rings, give rise to eigenproblems of very large dimensions. Solutions of such eigenproblems, which are both accurate and efficient, are very difficult. A method, based on combinatorial and group-theoretical considerations, leading to block diagonalization of the Hamiltonian matrix is proposed in this paper. For a given symmetry group of a Heisenberg Hamiltonian commuting with the total spin projection (i.e. with the total magnetization being a good quantum number) appropriate combinatorial and group-theoretical structures (partitions, orbits, stabilizers, etc.) are introduced and briefly discussed. Generation of these structures can be performed by means of slightly modified standard algorithms. The main ideas of these modification are presented in this paper. Possible applications of multiple precision libraries to eigenproblems are also mentioned.