William J. Massano

Ground-state energy of the Wolff model

Abstract Using the connected moments expansions (CMX) to third order, we have evaluated the ground-state energy of the single-impurity Wolff model. Comparisons are made with an equivalent Lanczos tridiagonalization truncation as well as second-order perturbation theory. All ranges of parameter space are considered with an isolated singularity arising in the CMX expansion.

Numerical analysis of moments expansions

Abstract We present numerical results for the estimate of the ground state energy for two quantum many-body systems using the connected moments expansion (CMX) and a newly developed alternate moments expansion (AMX). Comparisons are made with an equivalent Lanczos scheme which yields a variational upper bound for the ground state energy. For each system, the utility of both expansions is evaluated as they pertain to relevant regions of parameter space. A brief description of the (numerical) nature of the singularities which may arise in the series expansions is also given.

Ground-state of the linear anisotropic antiferromagnetic Heisenberg chain with nearest and next-nearest neighbor interactions

Abstract Using a modified Lanczos scheme, we evaluate the ground state properties of a sixteen-site one-dimensional spin- 1 2 Heisenberg antiferromagnet. We consider the case with nearest-neighbor antiferromagnetic interactions and next-nearest-neighbor ferromagnetic interactions as well as anisotropy. Comparisons are made with other exact results in the appropriate regions of parameter space.