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

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.