Model of Fractionalization of Faraday Lines in Compact Electrodynamics

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.

arXiv comment7 pages, 4 figures

References in corpus (8)

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• Dual Order Parameter for the Nodal Liquid
• Feasibility of self-correcting quantum memory and thermal stability of topological order
• Critical behaviour of the Ising model on the 4-dimensional lattice
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• Lattice Gerbe Theory
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Cited by in corpus (5)

• Dual gauge field theory of quantum liquid crystals in two dimensions
• Dual gauge field theory of quantum liquid crystals in three dimensions
• Sign-problem-free Monte Carlo simulation of certain frustrated quantum magnets
• Classification of nematic order in 2+1D: Dislocation melting and $O(2)/Z_N$ lattice gauge theory
• Model Realization and Numerical Studies of a Three-Dimensional Bosonic Topological Insulator and Symmetry-Enriched Topological Phases