  We construct defects in the XXZ and sine-Gordon models by making use of the
representation theory of quantum affine sl_2. The representations involved are
generalisations of the infinite-dimensional, q-oscillator representations used
in the construction of Q-operators. We present new results for intertwiners of
these representations, and use them to consider both quantum spin-chain
Hamiltonians with defects and quantum defects in the sine-Gordon model. We
connect specialisations our results with the work of Corrigan and Zambon on
type I and type II defects, and present sine-Gordon soliton/defect and
candidate defect/defect scattering matrices.
