Operator matrices generation: Combinatorial structures in finite spin models

Finite spin models, applicable in investigtion of mesoscopic rings, give ri se to eigenproblems of very large dimensions. Solutions of such eigenproble ms, which are both accurate and efficient, are very difficult. A method, ba sed on combinatorial. and group-theoretical considerations, leading to bloc k 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 nu mber) appropriate combinatorial and group-theoretical structures (partition s, orbits, stabilizers, etc.) are introduced and briefly discussed. Generat ion of these structures can be performed by means of slightly modified stan dard algorithms. The main ideas of these modification are presented in this paper. Possible applications of multiple precision libraries to eigenprobl ems are also mentioned. (C) 2001 Elsevier Science B.V. All rights reserved.