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

2010/06/08 by Robert Weston, Weston, Robert · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech #hep-th #math-ph #math.MP #math.QA

paper · pdf · doi:10.48550/arxiv.1006.1555

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

openalex publication_date 2010/06/08 · arxiv created 2010/06/28 · arxiv updated 2010/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct defects in the XXZ and sine-Gordon models by making use of the representation theory of quantum affine sl₂. 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.

Citations

• Eight-vertex model in lattice statistics and one-dimensional anisotropic heisenberg chain. I. Some fundamental eigenvectors
• Infinite conformal symmetry in two-dimensional quantum field theory
• Algebraic Approach in Unifying Quantum Integrable Models
• Eight-vertex model in lattice statistics and one-dimensional anisotropic heisenberg chain. III. Eigenvectors of the transfer matrix and hamiltonian
• Eight-vertex model in lattice statistics and one-dimensional anisotropic heisenberg chain. II. Equivalence to a generalized ice-type lattice model

Cited by

• Liouville integrable defects: the non-linear Schrödinger paradigm

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