Broken Symmetry and Fractionalized Flux Strings in a Staggered U(1) Pure Gauge Theory

Abstract

Inspired by self-adjoint extensions of the electric field operator in the Hamiltonian formalism, we extend the Wilsonian framework of Abelian lattice gauge theory by introducing a modified action parameterized by an angle $\hat{I}\pm$, where the ordinary Wilson theory corresponds to $\hat{I}\pm =0$. Choosing instead $\hat{I}\pm =\ddot{I}€$ (the "staggered" case) gives the only other theory in the family which preserves all symmetries of the original model at the microscopic level. We study the case of $3D$ $\mathrm{U}(1)$ pure gauge theory, simulating the staggered case of this model numerically in its dual formulation. We find evidence of a continuum limit with a spontaneously broken ${\mathbb{Z}}_2$ single-site translational symmetry, in contrast to the ordinary theory. Moreover, the confining string fractionalizes into multiple strands which separate spatial regions in distinct ground states of the broken symmetry.

18 pages, 10 figures