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Boundary K-matrices for the XYZ, XXZ AND XXX spin chains

Hector J. de Vega, A. González-Ruiz

Published Jun 18, 1993• 127 citations
OpenAlex

Abstract

The general solutions for the factorization equations of the reflection matrices $K^{\\pm}(\\theta)$ for the eight vertex and six vertex models (XYZ, XXZ and XXX chains) are found. The associated integrable magnetic Hamiltonians are explicitly derived, finding families dependig on several continuous as well as discrete parameters.

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EXACT BETHE ANSATZ SOLUTION FOR An−1 CHAINS WITH NON-SUq(n) INVARIANT OPEN BOUNDARY CONDITIONS

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arXiv:hep-th/9404141•Modern Physics Letters A•Aug 10, 1994•53 citations
The general solutions for the factorization equations of the reflection matrices Kpm(theta)K^{\\pm}(\\theta)Kpm(theta) for the eight vertex and six vertex models (XYZ, XXZ and XXX chains) are found. The associated integrable magnetic Hamiltonians are explicitly derived, finding families dependig on several continuous as well as discrete parameters.
Abstract The open XXZ spin chain with the anisotropy parameter Δ = − 1 2 and diagonal boundary magnetic fields that depend on a parameter x is studied. For real x > 0, the exact finite-size ground-state eigenvalue of the spin-chain Hamiltonian is explicitly computed. In a suitable normalisation, the ground-state components are characterised as polynomials in x with integer coefficients. Linear sum rules and special components of this eigenvector are explicitly computed in terms of determinant formulas. These results follow from the construction of a contour-integral solution to the boundary quantum Knizhnik–Zamolodchikov equations associated with the R -matrix and diagonal K -matrices of the six-vertex model. A relation between this solution and a weighted enumeration of totally-symmetric alternating sign matrices is conjectured.