The lattice Schwinger model as a discrete sum of filled Wilson loops

Abstract

Using techniques from hopping expansion we identically map the lattice Schwinger model with Wilson fermions to a model of oriented loops on the lattice. This is done by first computing the explicit form of the fermion determinant in the external field. Subsequent integration of the gauge fields renders a sum over all loop configurations with simple Gaussian weights depending on the number of plaquettes enclosed by the loops. In our new representation vacuum expectation values of local fermionic operators (scalars, vectors) can be computed by simply counting the loop flow through the sites (links) supporting the scalars (vectors). The strong coupling limit, possible applications of our methods to 4-D models and the introduction of a chemical potential are discussed.

Revised version, to appear in Nucl. Phys. B. More technical details, Comment on chemical potential shortened, references added

References in corpus (5)

• The Schwinger and Thirring models at finite chemical potential and temperature
• Evaluating Grassmann Integrals
• Loop representation for 2-D Wilson lattice fermions in a scalar background field
• A formula for the hopping expansion of 8-vertex models coupled to an external field
• The Worldsheet Formulation as an Alternative Method for Simulating Dynamical Fermions

Cited by in corpus (13)

• Approaches to the sign problem in lattice field theory
• Solving the sign problems of the massless lattice Schwinger model with a dual formulation
• Efficient simulation of relativistic fermions via vertex models
• Simulation strategies for the massless lattice Schwinger model in the dual formulation
• Fermion loop simulation of the lattice Gross-Neveu model
• Sum Rules for the Dirac Spectrum of the Schwinger Model
• Unexpected Results in the Chiral Limit with Staggered Fermions
• A formula for the hopping expansion of 8-vertex models coupled to an external field
• Dual simulation of the massless lattice Schwinger model with topological term and non-zero chemical potential
• A new way to deal with fermions in Monte Carlo simulations
• Computation of the phase induced by non-newtonian gravitational potentials in atom interferometry
• Isocliny in spinor space and Wilson fermions
• Fermion loop simulations in 2--d lattice theories -- results and limitations