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arXiv:1309.7785 · Nuclear Physics B

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

Pascal Baseilhac, Takeo Kojima

Published Jan 16, 2014• 28 citations
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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 〈σ1a〉 with a=z,± are obtained. Exploiting the spin-reversal property, relations between n-fold integrals of elliptic theta functions are extracted.

DOI
10.1016/j.nuclphysb.2014.01.011

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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 〈σ1a〉 with a=z,± are obtained. Exploiting the spin-reversal property, relations between n-fold integrals of elliptic theta functions are extracted.
The half-infinite XXZ spin chain with a triangular boundary is considered in the massive regime. Two integral representations of form factors of local operators are proposed using bosonization. Sufficient conditions such that the expressions for triangular boundary conditions coincide with those for diagonal boundary conditions are identified. The expressions are compared with known results upon specializations.Using the spin-reversal property which relates the Hamiltonian with upper and lower triangular boundary conditions, new identities between multiple integrals of infinite products are extracted.
The half-infinite XXZ spin chain with a triangular boundary is considered in the massive regime. Two integral representations of form factors of local operators are proposed using bosonization. Sufficient conditions such that the expressions for triangular boundary conditions coincide with those for diagonal boundary conditions are identified. The expressions are compared with known results upon specializations.Using the spin-reversal property which relates the Hamiltonian with upper and lower triangular boundary conditions, new identities between multiple integrals of infinite products are extracted.
The scalar products, form factors, and correlation functions of the XXZ spin chain with a twisted (or antiperiodic) boundary condition are obtained based on the inhomogeneous T–Q relation and the Bethe states constructed via the off-diagonal Bethe ansatz. It is shown that the scalar product of two off-shell Bethe states, the form factors, and the two-point correlation functions can be expressed as the summation of certain determinants. The corresponding homogeneous limits are studied. The results are also checked by the numerical calculations.