Chiral Symmetry Restoration in Anisotropic QED(3)

TL;DR

This study uses lattice Monte Carlo simulations to investigate how anisotropy affects chiral symmetry restoration in 3D QED, revealing a possibly crossover transition and persistent fermion mass.

Contribution

It provides the first detailed analysis of anisotropic effects on chiral symmetry and fermion properties in lattice QED3, with implications for high-temperature superconductivity models.

Findings

Chiral symmetry restoration point is strongly volume-dependent.

Scalar meson mass approaches pion mass at large anisotropy.

Fermion mass remains non-zero across studied anisotropy range.

Abstract

We present results from a Monte Carlo simulation of non-compact lattice QED in 3 dimensions in which an explicit anisotropy $\kappa$ between $x$ and $y$ hopping terms has been introduced into the action. Using a parameter set corresponding to broken chiral symmetry in the isotropic limit $\kappa=1$, we study the chiral condensate on $16^3$, $20^3$, and $24^3$ lattices as $\kappa$ is varied, and fit the data to an equation of state which incorporates anisotropic volume corrections. The value $\kappa_c$ at which chiral symmetry ispparently restored is strongly volume-dependent, suggesting that the transition may be a crossover rather than a true phase transition. In addition we present results on $16^3$ lattices for the scalar meson propagator, and for the Landau gauge-fixed fermion propagator. The scalar mass approaches the pion mass at large $\kappa$, consistent with chiral symmetry restoration, but the fermion remains massive at all values of $\kappa$ studied, suggesting that strong infra-red fluctuations persist into the chirally symmetric regime. Implications for models of high-$T_c$ superconductivity based on anisotropic QED$_3$ are discussed.