  We introduce an algebraic methodology for designing exactly-solvable Lie
model Hamiltonians. The idea consists in looking at the algebra generated by
bond operators. We illustrate how this method can be applied to solve numerous
problems of current interest in the context of topological quantum order. These
include Kitaev's toric code and honeycomb models, a vector exchange model, and
a Clifford gamma model on a triangular lattice.

Mesoscale and Nanoscale Physics;Statistical Mechanics