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

Author:

A. Banerjee, D. Banerjee, G. Kanwar, A. Mariani, T. Rindlisbacher, U. -J. Wiese

Keyword:

High Energy Physics - Lattice, High Energy Physics - Lattice (hep-lat), Strongly Correlated Electrons (cond-mat.str-el), High Energy Physics - Theory (hep-th), Quantum Physics (quant-ph)

journal:

date:

2023-09-28 16:00:00

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.

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