Improved finite-lattice estimates of the properties of two quantum spin models on the infinite square lattice

This paper describes an improvement in the method of exact diagonalization of Hamiltonians of quantum spin models on finite square lattices and the st atistical analysis of the data so obtained to estimate the physical propert ies of the models on the infinite square lattices at zero temperature. The geometry and topology of finite square lattices are described. The models s tudied are the spin one-half <it>XY</it> and Heisenberg antiferromagnets us ing 28 finite square lattices with up to 32 vertices. Our estimates of the energy and magnetization on each model on the infinite lattice at zero temp erature compare very well with recent estimates using quantum Monte Carlo, series expansion, and spin wave estimates. Estimates of spin wave velocity and transverse susceptibilities are more scattered.