Transition in the spectral gap of the massless overlap Dirac operator coupled to abelian fields in three dimensions

Abstract

The low lying spectrum of the massless overlap Dirac operator coupled to abelian fields in three dimensions with three different measures are shown to exhibit two phases: a strong coupling gapped phase and a weak coupling gapless phase. The vanishing of the gap from the strong coupling side with a Maxwell and a conformal measure is governed by a Gaussian exponent. Contrary to this result, the vanishing of the gap from the strong coupling side with a compact Thirring measure is not consistent with a Gaussian exponent. The low lying spectrum with a non-compact Thirring measure does not exhibit a simple non-monotonic behavior as a function of the lattice size on the weak coupling side. Our combined analysis suggests exploring the possibility of a strongly coupled continuum theory starting from a compact lattice Thirring model where a compact U(1) gauge field with a single link action is coupled to even number of flavors of massless overlap Dirac fermions.

18 pages, 5 figures

References in corpus (12)

• The electronic properties of graphene
• Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals
• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Level/rank Duality and Chern-Simons-Matter Theories
• UV fixed-point structure of the three-dimensional Thirring model
• Critical behavior of the (2+1)-dimensional Thirring model
• Critical Flavor Number in the Three Dimensional Thirring Model
• Numerical determination of monopole scaling dimension in parity-invariant three-dimensional non-compact QED
• Critical flavour number of the Thirring model in three dimensions
• Flavor and topological current correlators in parity-invariant three-dimensional QED
• Critical Behaviour in the Single Flavor Thirring Model in 2+1d
• QED${}_3$-inspired three-dimensional conformal lattice gauge theory without fine-tuning