Bloch Waves in Minimal Landau Gauge and the Infinite-Volume Limit of Lattice Gauge Theory

Abstract

By exploiting the similarity between Bloch's theorem for electrons in crystalline solids and the problem of Landau gauge-fixing in Yang-Mills theory on a "replicated" lattice, one is able to obtain essentially infinite-volume results from numerical simulations performed on a relatively small lattice. This approach, proposed by D. Zwanziger in \cite{Zwanziger:1993dh}, corresponds to taking the infinite-volume limit for Landau-gauge field configurations in two steps: firstly for the gauge transformation alone, while keeping the lattice volume finite, and secondly for the gauge-field configuration itself. The solutions to the gauge-fixing condition are then given in terms of Bloch waves. Applying the method to data from Monte Carlo simulations of pure SU(2) gauge theory in two and three space-time dimensions, we are able to evaluate the Landau-gauge gluon propagator for lattices of linear extent up to sixteen times larger than that of the simulated lattice. The approach is reminiscent of Fisher and Ruelle's construction of the thermodynamic limit in classical statistical mechanics.

4 pages, 1 figure (two plots)

References in corpus (6)

• Constraints on the IR behavior of the gluon propagator in Yang-Mills theories
• Constraints on the IR behavior of the ghost propagator in Yang-Mills theories
• Two- and three-point Green's functions in two-dimensional Landau-gauge Yang-Mills theory
• The gradient flow running coupling with twisted boundary conditions
• The Saga of Landau-Gauge Propagators: Gathering New Ammo
• Ghost sector and geometry in minimal Landau gauge: further constraining the infinite-volume limit

Cited by in corpus (6)

• QCD at finite temperature and chemical potential from Dyson-Schwinger equations
• Correlation functions of three-dimensional Yang-Mills theory from the FRG
• Constraining the gauge-fixed Lagrangian in minimal Landau gauge
• Probing the singularities of the Landau-gauge gluon and ghost propagators with rational approximants
• $H(4)$ tensor representations for the lattice Landau gauge gluon propagator and the estimation of lattice artefacts
• Restoring rotational invariance for lattice QCD propagators