ELSEVIER 21February1994 PhysicsLetters A 185 (1994) 435-439 PHYSICS LETTERS A Numerical analysis of moments expansions Jay D. Mancini 1, Yu Zhou, Peter F. Meier Department of Physics, Universityof Zurich, CH-8057Zurich, Switzerland William J. Massano Department of Science, State Universityof New York, Maritime College, Ft. Schuyler, Bronx, NY 10465, USA Janice D. Prie Department of Physics, Fordham University, Bronx, NY 10458, USA Received 21 September 1993;acceptedfor Publication 22 December 1993 Communicatedby J. Flouquet Abstract We present numerical results for the estimate of the ground state energy for two quantum many-body systems using the con- nected 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. 1. Introduction A number of years ago an analytic expansion for the ground state energy of any quantum system was developed by Cioslowski [ 1 ]. This connected mo- ments expansion (CMX) has its roots in the t-expan- sion theorem of Horn and Weinstein [ 2 ] and is re- lated to a cumulant expansion [ 3,4 ] thus giving it the property of being size-extensive. Although there have been numerous successes of the method cited in the literature (see, e.g., Ref. [ 5 ] ), there also exist many- body Hamiltonians for which, in certain regions of parameter space, singularities in the expansion may arise [6,7]. It should be emphasized that there are a Permanent address: Department of Physics, FordhamUniver- sity, Bronx, NY 10458,USA. number of attractive features to any series which arises from a moment expansion. These include fa- cility in constructing any order in the series because of the simple structure of the recursive algorithm, the series to any order is size-extensive and, unlike for perturbational techniques, there is no ambiguity in the partitioning of the Hamiltonian into strong and weak terms and no problems with (quasi-) degener- act of the eigenfunctions of the unperturbed Hamiltonian. Recently Mancini, Zhou and Meier [ 8 ] have pre- sented an in-depth theoretical study of a certain class of moments expansion. Several properties of the con- nected moments expansion were discussed as well as an analytic proof of the cancellation of singularities to all orders of the expansion. Also presented was the derivation of an alternate moments expansion 0375-9601/94/$07.00 © 1994ElsevierScienceB.V. All rights reserved SSDI0375-9601 (93)E1032-B