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We construct defects in the XXZ and sine-Gordon models by making use of therepresentation theory of quantum affine sl_2. The representations involved aregeneralisations of the infinite-dimensional, q-oscillator representations usedin the construction of Q-operators. We present new results for intertwiners ofthese representations, and use them to consider both quantum spin-chainHamiltonians with defects and quantum defects in the sine-Gordon model. Weconnect specialisations our results with the work of Corrigan and Zambon ontype I and type II defects, and present sine-Gordon soliton/defect andcandidate defect/defect scattering matrices.

An Algebraic Setting for Defects in the XXZ and Sine-Gordon Models