The Phase Diagram of Compact QED Coupled to a Four-Fermi Interaction

TL;DR

This study maps the phase diagram of compact QED with four fermion species, revealing distinct monopole and chiral transitions, with implications for understanding critical phenomena and fixed points in lattice gauge theories.

Contribution

It provides the first high-statistics simulation of massless QED with four fermions in the chiral limit, identifying the order of phase transitions and discussing universality class challenges.

Findings

Monopole condensation transition is first order.

Chiral transition is second order.

Critical indices deviate from mean field predictions.

Abstract

Compact lattice Quantum Electrodynamics (QED) with four species of fermions is simulated with massless quarks by using the $\chi$QED scheme of adding a four-fermi interaction to the action. Simulations directly in the chiral limit of massless quarks are done with high statistics on $8^4$, and $16^4$ lattices, and the phase diagram, parameterized by the gauge and the four-fermi couplings, is mapped out. The line of monopole condensation transitions is separate from the line of chiral symmetry restoration. The simulation results indicate that the monopole condensation transition is first order while the chiral transition is second order. The challenges in determining the Universality class of the chiral transition are discussed. If the scaling region for the chiral transition is sufficiently wide, the $16^4$ simulations predict critical indices far from mean field values. We discuss a speculative scenario in which anti-screening provided by double-helix strands of monopole and anti-monopole loops are the agent that balances the screening of fermion anti-fermion pairs to produce an ultra-violet fixed point in the electric coupling.