Plaquette expansion in lattice Hamiltonian models

Journal Article · Sun Feb 14 23:00:00 EST 1993 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.47.1640· OSTI ID:6993640

Hollenberg, L C.L. ^[1]

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1. Research Centre for High Energy Physics, School of Physics, University of Melbourne, Parkville, Victoria 3052 (Australia)

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 [l angle][ital H][sup [ital n]][r angle][sub [ital c]] and the number of plaquettes, [ital N][sub [ital p]], are obtained. Expansions in 1/[ital N][sub [ital p]] suggest a very simple general form for the first few terms in the 1/[ital N][sub [ital p]] expansions for all [alpha][sub [ital n]] and [beta][sub [ital n]]. For the one-dimensional Heisenberg spin chain it is demonstrated that the ground-state eigenvalue of the tridiagonal Lanczos matrix derived from this plaquette expansion approaches the true infinite lattice limit as the number of terms in the plaquette expansion is increased.

• OSTI ID: 6993640
• Journal Information: Physical Review, D (Particles Fields); (United States), Journal Name: Physical Review, D (Particles Fields); (United States) Vol. 47:4; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

662110* -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
662230 -- Quantum Chromodynamics-- (1992-)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANGULAR MOMENTUM
CRYSTAL MODELS
EIGENVALUES
ENERGY DENSITY
FIELD THEORIES
HAMILTONIANS
HEISENBERG MODEL
LATTICE FIELD THEORY
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MATRICES
ONE-DIMENSIONAL CALCULATIONS
PARTICLE PROPERTIES
QUANTUM CHROMODYNAMICS
QUANTUM FIELD THEORY
QUANTUM OPERATORS
SPIN