Model of Fractionalization of Faraday Lines in Compact Electrodynamics

TL;DR

This paper introduces a novel phase in compact quantum electrodynamics where excitations are fractionalized, leading to new topological phenomena and fractionalized Faraday lines, demonstrated through Monte Carlo simulations.

Contribution

It constructs a lattice gauge theory model showing fractionalization of Faraday lines with N-tupled monopole condensation and explores associated topological excitations.

Findings

Existence of fractionalized Faraday lines in CQED.

Demonstration of N-tupled monopole condensation leading to fractionalization.

Monte Carlo simulations confirming the phase in (3+1) dimensions.

Abstract

Motivated by ideas of fractionalization and intrinsic topological order in bosonic models with short-range interactions, we consider similar phenomena in formal lattice gauge theory models. Specifically, we show that a compact quantum electrodynamics (CQED) can have, besides the familiar Coulomb and confined phases, additional unusual confined phases where excitations are quantum lines carrying fractions of the elementary unit of electric field strength. We construct a model that has $N$-tupled monopole condensation and realizes $1/N$ fractionalization of the quantum Faraday lines. This phase has another excitation which is a $Z_N$ quantum surface in spatial dimensions five and higher, but can be viewed as a quantum line or a quantum particle in four or three spatial dimensions respectively. These excitation have statistical interactions with the fractionalized Faraday lines; for example, in three spatial dimensions, the particle excitation picks up a Berry phase of $e^{i2\pi/N}$ when going around the fractionalized Faraday line excitation. We demonstrate the existence of this phase by Monte Carlo simulations in (3+1) space-time dimensions.