## Abstract

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{sup n}){sub c}, and the number of plaquettes, N{sub p}, are obtained. Expansions in 1/N{sub p} suggest a very simple general form for the first few terms in the 1/N{sub p} expansions for all {alpha}{sub n} and {beta}{sub n}. For the one dimensional Heisenberg spin-chain it is demonstrated that the ground-state eigenvalue of the tri-diagonal Lanczos matrix derived from this plaquette expansion approaches the true infinite lattice limit as the number of terms in the plaquette expansion is increased. 8 refs., 5 figs.

## Citation Formats

Hollenberg, L C.L.
Plaquette expansion in lattice Hamiltonian models.
Australia: N. p.,
1992.
Web.

Hollenberg, L C.L.
Plaquette expansion in lattice Hamiltonian models.
Australia.

Hollenberg, L C.L.
1992.
"Plaquette expansion in lattice Hamiltonian models."
Australia.

@misc{etde_10109010,

title = {Plaquette expansion in lattice Hamiltonian models}

author = {Hollenberg, L C.L.}

abstractNote = {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{sup n}){sub c}, and the number of plaquettes, N{sub p}, are obtained. Expansions in 1/N{sub p} suggest a very simple general form for the first few terms in the 1/N{sub p} expansions for all {alpha}{sub n} and {beta}{sub n}. For the one dimensional Heisenberg spin-chain it is demonstrated that the ground-state eigenvalue of the tri-diagonal Lanczos matrix derived from this plaquette expansion approaches the true infinite lattice limit as the number of terms in the plaquette expansion is increased. 8 refs., 5 figs.}

place = {Australia}

year = {1992}

month = {Jul}

}

title = {Plaquette expansion in lattice Hamiltonian models}

author = {Hollenberg, L C.L.}

abstractNote = {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{sup n}){sub c}, and the number of plaquettes, N{sub p}, are obtained. Expansions in 1/N{sub p} suggest a very simple general form for the first few terms in the 1/N{sub p} expansions for all {alpha}{sub n} and {beta}{sub n}. For the one dimensional Heisenberg spin-chain it is demonstrated that the ground-state eigenvalue of the tri-diagonal Lanczos matrix derived from this plaquette expansion approaches the true infinite lattice limit as the number of terms in the plaquette expansion is increased. 8 refs., 5 figs.}

place = {Australia}

year = {1992}

month = {Jul}

}