Lattice Study of Anisotropic QED-3

TL;DR

This study uses lattice Monte Carlo simulations to investigate how anisotropy affects the phase structure of QED3, revealing that anisotropy is a relevant deformation and identifying a chiral symmetry restoring transition.

Contribution

It provides the first non-perturbative lattice evidence that anisotropy in QED3 is a relevant deformation, contrasting with previous analytic predictions.

Findings

Renormalised anisotropy exceeds explicit anisotropy

Chiral symmetry restoring transition at κ ≈ 4.5

Pseudogap phase persists down to T=0 in cuprates

Abstract

We present results from a Monte Carlo simulation of non-compact lattice QED in 3 dimensions on a $16^3$ lattice in which an explicit anisotropy between $x$ and $y$ hopping terms has been introduced into the action. This formulation is inspired by recent formulations of anisotropic QED$_3$ as an effective theory of the non-superconducting portion of the cuprate phase diagram, with relativistic fermion degrees of freedom defined near the nodes of the gap function on the Fermi surface, and massless photon degrees of freedom reproducing the dynamics of the phase disorder of the superconducting order parameter. Using a parameter set corresponding to broken chiral symmetry in the isotropic limit, our results show that the renormalised anisotropy, defined in terms of the ratio of correlation lengths of gauge invariant bound states in the $x$ and $y$ directions, exceeds the explicit anisotropy $\kappa$ introduced in the lattice action, implying in contrast to recent analytic results that anisotropy is a relevant deformation of QED$_3$. There also appears to be a chiral symmetry restoring phase transition at $\kappa_c\simeq4.5$, implying that the pseudogap phase persists down to T=0 in the cuprate phase diagram.