## 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.

## 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}

}

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}

}