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

TL;DR

This paper introduces a modified Abelian lattice gauge theory with a new parameter, revealing a phase with broken symmetry and fractionalized flux strings in 3D U(1) gauge theory.

Contribution

It extends the Wilsonian framework by adding a parameter that preserves symmetries and uncovers a novel phase with fractionalized flux strings and broken translational symmetry.

Findings

Evidence of a continuum limit with broken Z2 symmetry

Observation of fractionalized confining strings

Numerical simulation in dual formulation

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 $\alpha$, where the ordinary Wilson theory corresponds to $\alpha=0$. Choosing instead $\alpha=\pi$ (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.