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

Journal Article · Sat Oct 15 04:00:00 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), Journal Name: Phys. Rev. D; (United States) Vol. 28:8; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

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