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A general non-perturbative estimate of the energy density of lattice Hamiltonians

Technical Report:

Abstract

Employing a theorem on lower bounds on the zeros of orthogonal polynomials, the plaquette expansion to order 1/N{sub p} of the tri-diagonal Lanczos matrix elements is solved for the ground state energy density in the infinite lattice limit. The resulting non-perturbative expression for the estimate of the energy density in terms of the connected coefficients to order {sub c} is completely general. This expression is applied to various Hamiltonian systems - the Heisenberg model in D dimensions and SU(2) and SU(3) lattice gauge theory in 3 + 1 dimensions. In all cases the analytic estimate to the energy density is not only a significant improvement on the trial state, but is typically accurate to a few percent. The energy density of the D-dimensional Heisenberg model is predicted to approach {epsilon}{sub 0}(Neel) - 1/8 for large D. In the case of SU(2) and SU(3) the specific heat derived from the energy density peaks at the correct strong to weak coupling transition. 12 refs., 1 tab., 2 figs.
Publication Date:
Dec 31, 1994
Product Type:
Technical Report
Report Number:
UM-P-93/90
Reference Number:
SCA: 662110; PA: AIX-26:017896; EDB-95:032206; SN: 95001330006
Resource Relation:
Other Information: PBD: [1994]
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; HEISENBERG MODEL; ENERGY DENSITY; HAMILTONIANS; LATTICE FIELD THEORY; ANALYTICAL SOLUTION; GROUND STATES; MANY-BODY PROBLEM; MATRIX ELEMENTS; SU GROUPS; THEORETICAL DATA; 662110; THEORY OF FIELDS AND STRINGS
Sponsoring Organizations:
Australian Research Council, Canberra, ACT (Australia)
OSTI ID:
10113733
Research Organizations:
Melbourne Univ., Parkville, VIC (Australia). School of Physics
Country of Origin:
Australia
Language:
English
Other Identifying Numbers:
Other: ON: DE95616283; TRN: AU9414206017896
Availability:
OSTI; NTIS (US Sales Only); INIS
Submitting Site:
INIS
Size:
14 p.
Announcement Date:
Jun 30, 2005

Technical Report:

Citation Formats

Hollenberg, L C.L., and Witte, N S. A general non-perturbative estimate of the energy density of lattice Hamiltonians. Australia: N. p., 1994. Web.
Hollenberg, L C.L., & Witte, N S. A general non-perturbative estimate of the energy density of lattice Hamiltonians. Australia.
Hollenberg, L C.L., and Witte, N S. 1994. "A general non-perturbative estimate of the energy density of lattice Hamiltonians." Australia.
@misc{etde_10113733,
title = {A general non-perturbative estimate of the energy density of lattice Hamiltonians}
author = {Hollenberg, L C.L., and Witte, N S}
abstractNote = {Employing a theorem on lower bounds on the zeros of orthogonal polynomials, the plaquette expansion to order 1/N{sub p} of the tri-diagonal Lanczos matrix elements is solved for the ground state energy density in the infinite lattice limit. The resulting non-perturbative expression for the estimate of the energy density in terms of the connected coefficients to order {sub c} is completely general. This expression is applied to various Hamiltonian systems - the Heisenberg model in D dimensions and SU(2) and SU(3) lattice gauge theory in 3 + 1 dimensions. In all cases the analytic estimate to the energy density is not only a significant improvement on the trial state, but is typically accurate to a few percent. The energy density of the D-dimensional Heisenberg model is predicted to approach {epsilon}{sub 0}(Neel) - 1/8 for large D. In the case of SU(2) and SU(3) the specific heat derived from the energy density peaks at the correct strong to weak coupling transition. 12 refs., 1 tab., 2 figs.}
place = {Australia}
year = {1994}
month = {Dec}
}