Phase Structure of a 3D Nonlocal U(1) Gauge Theory: Deconfinement by Gapless Matter Fields

TL;DR

This study investigates how nonlocal interactions in a 3D U(1) gauge theory influence phase transitions, revealing that gapless matter fields can induce deconfinement, with phase behavior depending on the decay of nonlocal couplings.

Contribution

It demonstrates that nonlocal interactions simulating gapless matter fields can lead to deconfinement in 3D U(1) gauge theories, highlighting the role of nonlocal coupling decay in phase transitions.

Findings

Power-decaying couplings induce second-order phase transitions to deconfinement.

Exponentially-decaying couplings do not show signs of phase transition.

Massless matter fields can destabilize confinement in 3D U(1) gauge theories.

Abstract

In this paper, we study a 3D compact U(1) lattice gauge theory with a variety of nonlocal interactions that simulates the effects of gapless/gapful matter fields. This theory is quite important to investigate the phase structures of QED$_3$ and strongly-correlated electron systems like the 2D quantum spin models, the fractional quantum Hall effect, the t-J model of high-temperature superconductivity. We restrict the nonlocal interactions among gauge variables only to those along the temporal direction and adjust their coupling constants optimally to simulate the isotropic nonlocal couplings of the original models. We perform numerical studies of the model to find that, for a certain class of power-decaying couplings, there appears a second-order phase transition to the deconfinement phase as the gauge coupling constant is decreased. On the other hand, for the exponentially-decaying coupling, there are no signals for second-order phase transition. These results indicate the possibility that introduction of sufficient number of massless matter fields destabilizes the permanent confinement in the 3D compact U(1) pure gauge theory due to instantons.