On the Yang-Baxter equation for the six-vertex model

Vladimir V. Mangazeev*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    52 Citations (Scopus)

    Abstract

    In this paper we review the theory of the Yang-Baxter equation related to the 6-vertex model and its higher spin generalizations. We employ a 3D approach to the problem. Starting with the 3D R-matrix, we consider a two-layer projection of the corresponding 3D lattice model. As a result, we obtain a new expression for the higher spin R-matrix associated with the affine quantum algebra Uq(sl(2)̂). In the simplest case of the spin s= 1/2 this R-matrix naturally reduces to the R-matrix of the 6-vertex model. Taking a special limit in our construction we also obtain new formulas for the Q-operators acting in the representation space of arbitrary (half-)integer spin. Remarkably, this construction can be naturally extended to any complex values of spin s. We also give all functional equations satisfied by the transfer-matrices and Q-operators.

    Original languageEnglish
    Pages (from-to)70-96
    Number of pages27
    JournalNuclear Physics B
    Volume882
    Issue number1
    DOIs
    Publication statusPublished - May 2014

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