Correlation functions of the half-infinite XXZ spin chain with a triangular boundary

Abstract

The half-infinite XXZ spin chain with a triangular boundary is considered in the massive regime. Two integral representations of correlation functions are proposed using bosonization. Sufficient conditions such that the expressions for triangular boundary conditions coincide with those for diagonal boundary conditions are identified. As an application, summation formulae of the boundary expectation values $⟨{\sigma }_1^a⟩$ with $a=z,\pm$ are obtained. Exploiting the spin-reversal property, relations between $n$-fold integrals of elliptic theta functions are extracted.

38 pages

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Cited by in corpus (17)

• Modified algebraic Bethe ansatz for XXZ chain on the segment - I - triangular cases
• Non-Abelian symmetries of the half-infinite XXZ spin chain
• Koornwinder polynomials and the XXZ spin chain
• The alternating central extension of the $q$-Onsager algebra
• The alternating presentation of $U_q(\widehat{g{l}_2})$ from Freidel-Maillet algebras
• Separation of variables bases for integrable $g{l}_{\mathcal{M}|\mathcal{N}}$ and Hubbard models
• Boundary quantum Knizhnik-Zamolodchikov equations and fusion
• Form factors of the half-infinite XXZ spin chain with a triangular boundary
• Off-shell scalar products for the $XXZ$ spin chain with open boundaries
• Symmetric functions and wavefunctions of the six-vertex model by Izergin-Korepin analysis
• A conjecture concerning the $q$-Onsager algebra
• Exact solutions of the $C_n$ quantum spin chain
• A bispectral q-hypergeometric basis for a class of quantum integrable models
• Connection problems for quantum affine KZ equations and integrable lattice models
• A representation basis for the quantum integrable spin chain associated with the su(3) algebra
• Bethe States of the integrable spin-s chain with generic open boundaries
• Using a $q$-shuffle algebra to describe the basic module $V({\Lambda }_0)$ for the quantized enveloping algebra $U_q({\widehat{\mathfrak{sl}}}_2)$