On the origin of artificial electrodynamics and other stories in three-dimensional bosonic models

Abstract

Several simple models of strongly correlated bosons on three-dimensional lattices have been shown to possess exotic fractionalized Mott insulating phases with a gapless `photon' excitation. In this paper we show how to view the physics of this `Coulomb' state in terms of the excitations of proximate superfluid. We argue for the presence of ordered vortex cores with a broken discrete symmetry in the nearby superfluid phase, and that proliferating these degenerate but distinct vortices with equal amplitudes produces the Coulomb phase. This provides a simple physical description of the origin of the exotic excitations of the Coulomb state. The physical picture is formalized by means of a dual description of three-dimensional bosonic systems in terms of fluctuating quantum mechanical vortex loops. Such a dual formulation is extensively developed. It is shown how the Coulomb phase (as well as various other familiar phases) of three-dimensional bosonic systems may be described in this vortex loop theory. For bosons at half-filling and the closely related system of spin-1/2 quantum magnets on a cubic lattice, fractionalized phases as well as bond or `box' ordered states are possible. The latter are analyzed by an extension of techniques previously developed in two spatial dimensions. The relation between these `confining' phases with broken translational symmetry and the fractionalized Coulomb phase is exposed.