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

Abstract

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.

16 pages, 14 figures. The updated version contains substantial changes to connect with the recent work of Corrigan and Zambon on type II sine-Gordon defects, and to include further references

References in corpus (5)

• Hidden Grassmann Structure in the XXZ Model II: Creation Operators
• Quantum and classical integrable sine-Gordon model with defect
• Solving topological defects via fusion
• The two-spinon transverse structure factor of the gapped Heisenberg antiferromagnetic chain
• Solving Baxter's TQ-equation via representation theory