General nonperturbative estimate of the energy density of lattice Hamiltonians

Journal Article · Thu Sep 01 04:00:00 EDT 1994 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.50.3382· OSTI ID:7241999

Hollenberg, L C.L.; Witte, N S ^[1]

---

1. School of Physics, University of Melbourne, Parkville, Victoria 3052 (Australia)

Employing a theorem on lower bounds on the zeros of orthogonal polynomials, the plaquette expansion to order 1/[ital N][sub [ital p]] of the tridiagonal Lanczos matrix elements is solved for the ground-state energy density in the infinite lattice limit. The resulting nonperturbative expression for the estimate of the energy density in terms of the connected coefficients to order [l angle][ital H][sup 4][r angle][sub [ital c]] is completely general. This expression is applied to various Hamiltonian systems---the Heisenberg model in [ital 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 [ital D]-dimensional Heisenberg model is predicted to approach [ital scrE][sub 0](Neel)[minus]1/8 for large [ital 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.

• OSTI ID: 7241999
• Journal Information: Physical Review, D (Particles Fields); (United States), Journal Name: Physical Review, D (Particles Fields); (United States) Vol. 50:5; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

661300* -- Other Aspects of Physical Science-- (1992-)
662110 -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CRYSTAL MODELS
ENERGY DENSITY
ENERGY LEVELS
FIELD THEORIES
GAUGE INVARIANCE
GROUND STATES
HAMILTONIANS
HEISENBERG MODEL
INVARIANCE PRINCIPLES
LATTICE FIELD THEORY
LIE GROUPS
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MATRIX ELEMENTS
QUANTUM FIELD THEORY
QUANTUM OPERATORS
SU GROUPS
SU-2 GROUPS
SU-3 GROUPS
SYMMETRY GROUPS