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

TL;DR

This paper develops a dual vortex loop theory to explain the origin of exotic Coulomb phases in three-dimensional bosonic models, linking fractionalization, symmetry breaking, and vortex proliferation.

Contribution

It introduces a dual vortex loop framework to describe Coulomb and other phases in 3D bosonic systems, revealing the role of vortex core ordering in phase transitions.

Findings

Coulomb phase arises from proliferating ordered vortex cores.

Dual vortex loop theory effectively describes various phases.

Fractionalized and symmetry-broken phases are interconnected.

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.