Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

International Journal of Quantum Chemistry

Variational localized‐site cluster expansions. VII. Higher ansätze and the linear heisenberg model

M. A. García‐Bach, Daniel Klein

Published Aug 1, 1977• 19 citations
Publisher

Abstract

Abstract The localized‐site cluster expansion technique is applied to the infinite linear Heisenberg model with both nearest‐neighbor and next nearest‐neighbor interactions. These cluster ansätze are systematically studied and improved, up to the so‐called 5‐site approximation. Generally we find the present cluster ansätze yield the most accurate variational results yet available.

DOI
10.1002/qua.560120205

Related papers

Variational localized‐site cluster expansions. VI. General theory revisited

Douglas J. Klein

Abstract A general and systematic localized‐site cluster expansion is described. It provides simple physically appealing and computationally feasible wave function ansätze, as well as, via extension of the cluster expansion, a unique expression for general, possibly exact, wave functions. We show that a variety of matrix element evaluation techniques are available and that they are sometimes exact though relatively simple. These techniques often proceed in terms of computational time proportional to the number of different types of sites, rather than their total number. Thus it seems we have a new and viable many‐body theory, which is expected to be most accurate and most readily implementable when a physical picture with slightly perturbed localized sites is relevant.

International Journal of Quantum Chemistry•Aug 1, 1977•11 citations

Variational localized-site cluster expansions

Daniel Klein

The simplest localized-site cluster expansion for a system of doublet sites described within the context of a valence bond or Heisenberg model is considered. Exact matrix element formulae are obtained for a variety of systems, including some with fused rings. Numerical results for the linear chain case suggest that this simple ansatz improves over the common resonance theory presumption of Kekulé structures only.

Molecular Physics•Mar 1, 1976•11 citations

Variational localized-site cluster expansions

Daniel Klein, M. A. García‐Bach

The simplest variational localized-site cluster expansions for Hubbard and Pariser-Parr-Pople (PPP) models are considered and explicit matrix element formulae are developed. Numerical calculations for infinite chains and finite cycles are reported. It is found that even the simplest ansatz yields results in the atomic limit which are better than other conventional techniques. Near the band limit its accuracy decreases, as expected, but the next most simple ansatz does better.

Molecular Physics•Mar 1, 1976•7 citations

Variational localized-site cluster expansions. XI. Coherent state derivation of effective heisenberg hamiltonians

Douglas J. Klein, W. A. Seitz, M. A. García‐Bach +2 more

A variational derivation of Heisenberg or valence-bond models from a Hubbard (or Pariser-Parr-Pople) Hamiltonian is described. Calculations within a low-order approximation are carried out for linear-chain and graphite lattices. The results seem to be quite accurate with little computational effort when compared with other approaches.

International Journal of Quantum Chemistry•Jul 9, 2009•1 citation

Cluster-expansion representation

M. A. García‐Bach, Daniel Klein

We describe how starting from a type of nearest-neighbour localized wavefunction cluster expansion one may conveniently build up a locally correlated orthonormal `many-body' basis for a linear-chain system. The initial correlated cluster expansion approximant to the ground state plays the role of a `vacuum' while the other members of the basis are single or multiple excitations above this. The scheme is illustrated for the case of two states per site, in application to the linear-chain Heisenberg model.

Journal of Physics A Mathematical and General•Jan 7, 1996•4 citations

Variational localized-site cluster expansions. II. Trees and near trees

Douglas J. Klein, M. A. García‐Bach

Cluster expanded wavefunctions involving localized-site states and only pair excitations between nearest neighbor sites are considered. In the case that the bonds connecting these nearest neighbor sites form a tree graph (without rings), exact matrix element formulas are obtained in terms of the inverse of a modified type of topological matrix associated with this tree graph. The treatment of some near-tree cases, without any touching rings, is also discussed.

The Journal of Chemical Physics•Jun 15, 1976•8 citations
Abstract The localized‐site cluster expansion technique is applied to the infinite linear Heisenberg model with both nearest‐neighbor and next nearest‐neighbor interactions. These cluster ansätze are systematically studied and improved, up to the so‐called 5‐site approximation. Generally we find the present cluster ansätze yield the most accurate variational results yet available.
Abstract A general and systematic localized‐site cluster expansion is described. It provides simple physically appealing and computationally feasible wave function ansätze, as well as, via extension of the cluster expansion, a unique expression for general, possibly exact, wave functions. We show that a variety of matrix element evaluation techniques are available and that they are sometimes exact though relatively simple. These techniques often proceed in terms of computational time proportional to the number of different types of sites, rather than their total number. Thus it seems we have a new and viable many‐body theory, which is expected to be most accurate and most readily implementable when a physical picture with slightly perturbed localized sites is relevant.
We describe how starting from a type of nearest-neighbour localized wavefunction cluster expansion one may conveniently build up a locally correlated orthonormal `many-body' basis for a linear-chain system. The initial correlated cluster expansion approximant to the ground state plays the role of a `vacuum' while the other members of the basis are single or multiple excitations above this. The scheme is illustrated for the case of two states per site, in application to the linear-chain Heisenberg model.