Exactly Solvable Models Of Spin Liquids With Spinons, And Of Three-Dimensional Topological Paramagnets

We develop a scheme to make exactly solvable gauge theories whose electric flux lines host (1+1)-dimensional topological phases. We use this exact "decorated-string-net" framework to construct several classes of interesting models. In particular, we construct an exactly solvable model of a quantum spin liquid whose (gapped) elementary excitations form doublets under an internal symmetry, and hence may be regarded as spin-carrying spinons. The model may be formulated, and is solvable, in any number of dimensions on any bipartite graph. Another example, in any dimension, has Z(2) topological order and anyons which are Kramers' doublets of time-reversal symmetry. Further, we make exactly solvable models of three-dimensional topological paramagnets.