A Bionic Coulomb Phase on the Pyrochlore Lattice

Abstract

A class of three dimensional classical lattice systems with macroscopic ground state degeneracies, most famously the spin ice system, are known to exhibit "Coulomb" phases wherein long wavelength correlations within the ground state manifold are described by an emergent Maxwell electrodynamics. We discuss a new example of this phenomenon-the four state Potts model on the pyrochlore lattice-where the long wavelength description now involves three independent gauge fields as we confirm via simulation. The excitations above the ground state manifold are bions, defects that are simultaneously charged under two of the three gauge fields, and exhibit an entropic interaction dictated by these charges. We also show that the distribution of flux loops shows a scaling with loop length and system size previously identified as characteristic of Coulomb phases.

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• Length Distributions in Loop Soups
• Confinement of monopoles and scaling theory near unconventional critical points
• A Classical Chiral Spin-Liquid from Chiral Interactions on the Pyrochlore Lattice
• Color ice states, weathervane modes, and order by disorder in the bilinear-biquadratic pyrochlore Heisenberg antiferromagnet
• Four-coloring model and frustrated superfluidity in the diamond lattice
• Entanglement dynamics in monitored Kitaev circuits: loop models, symmetry classification, and quantum Lifshitz scaling
• Universal statistics of vortex tangle in three-dimensional wave chaos
• Classical ${\mathbb{Z}}_2$ spin liquid on the generalized four-color Kitaev model