Topology of the Vacuum

Abstract

Before being known for the emergence of monopoles, spin ice draw the attention of the community for its extensively degenerate ground state. We have seen in previous chapters how a Coulomb gauge field emerges from the coarse-graining of this ground state. It is the goal of this chapter to connect this field-theory picture with its topological nature. In this context, spin ice is a three-dimensional vertex model, divided into topological sectors. Topological sectors are connected between each other via string updates. These strings may become the intrinsic excitations of exotic phase transitions when the degeneracy of the Coulomb phase is lifted, and can be mapped onto world lines for bosons in the corresponding quantum problem in (2+1) dimensions. As an alternative point of view, we will also discuss how the spin-ice ground state is equivalent to a fully packed loop model, whose statistics is reminiscent of critical percolation and Brownian motion in two and three dimensions respectively.