Application of the Green's-function Monte Carlo method to the compact Abelian lattice gauge theory

Journal Article · Sat Oct 15 00:00:00 EDT 1983 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.28.2067· OSTI ID:5467773

Heys, D W; Stump, D R

We have applied the Green's-function Monte Carlo (GFMC) method to the Hamiltonian formulation of the compact U(1) lattice gauge theory in three and two (space) dimensions on small lattices, 3 x 3 x 3 and 5 x 5. The GFMC method is a Monte Carlo method of finding the ground state of a quantum-mechanical system with many degrees of freedom, by iteration of an integral operator of which the ground state is an eigenstate. An interesting aspect of this method is an importance-sampling technique that makes use of a trial wave function to accelerate convergence of the Monte Carlo estimates. We used two importance functions in these calculations, which were designed to be accurate in the small- and large-coupling limits. These importance functions were optimized by the variational principle; the results of the variational calculations are interesting in their own right. Our Monte Carlo results exhibit evidence of the phase transition of the three-dimensional compact U(1) lattice gauge theory, and indicate the nonexistence of a phase transition in the two-dimensional theory.

• Research Organization: Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824
• OSTI ID: 5467773
• Journal Information: Phys. Rev. D; (United States), Vol. 28:8
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
LATTICE FIELD THEORY
GAUGE INVARIANCE
MONTE CARLO METHOD
EIGENSTATES
FEYNMAN PATH INTEGRAL
GREEN FUNCTION
HAMILTONIANS
QUANTUM CHROMODYNAMICS
QUANTUM MECHANICS
U-1 GROUPS
VARIATIONAL METHODS
WAVE FUNCTIONS
FIELD THEORIES
FUNCTIONS
INTEGRALS
INVARIANCE PRINCIPLES
LIE GROUPS
MATHEMATICAL OPERATORS
MECHANICS
QUANTUM FIELD THEORY
QUANTUM OPERATORS
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U GROUPS
645400* - High Energy Physics- Field Theory