Exactly solvable two-dimensional quantum spin models

A method is proposed for constructing an exact ground-state wave function o f a two-dimensional model with spin 1/2. The basis of the method is to repr esent the wave function by a product of fourth-rank spinors associated with the nodes of a lattice and the metric spinors corresponding to bonds betwe en nearest neighbor nodes. The function so constructed is an exact wave fun ction of a 14-parameter model. The special case of this model depending on one parameter is analyzed in detail. The ground state is always a nondegene rate singlet, and the spin correlation functions decay exponentially with d istance. The method can be generalized for models with spin 1/2 to other ty pes of lattices. (C) 1999 American Institute of Physics. [S1063-7761(99)022 01-5].