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Plaquette expansion in lattice Hamiltonian models

Technical Report:

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.
Publication Date:
Jul 06, 1992
Product Type:
Technical Report
Report Number:
UM-P-92/46; OZ-92/18.
Reference Number:
SCA: 661100; PA: AIX-24:003178; SN: 93000913696
Resource Relation:
Other Information: PBD: 6 Jul 1992
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; GROUND STATES; EIGENVALUES; HEISENBERG MODEL; MATHEMATICAL OPERATORS; ENERGY DENSITY; EXPERIMENTAL DATA; HAMILTONIANS; MATRICES; SERIES EXPANSION; 661100; CLASSICAL AND QUANTUM MECHANICS
OSTI ID:
10109010
Research Organizations:
Melbourne Univ., Parkville, VIC (Australia). School of Physics
Country of Origin:
Australia
Language:
English
Other Identifying Numbers:
Other: ON: DE93609846; TRN: AU9212951003178
Availability:
OSTI; NTIS (US Sales Only); INIS
Submitting Site:
INIS
Size:
[16] p.
Announcement Date:
Jun 30, 2005

Technical Report:

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}
}