PLAQUETTE EXPANSION IN LATTICE HAMILTONIAN MODELS

The Lanczos method in operator form is applied to a general lattice Hamiltonian and expressions for the first few Lanczos matrices in terms of the connected Hamiltonian moments [H(n)]c, and the number of plaquettes, N(p), are obtained. Expansions in 1/N(p) suggest a very simple general form for the first few terms in the 1/N(p) expansions for all alpha(n), and beta(n). For the one-dimensional Heisenberg spin chain it is demonstrated that the ground-state eigenvalue of the tridiagonal Lanczos matrix derived from this plaquette expansion approaches the true infinite lattice limit as the number of terms in the plaquette expansion is increased.