Yang-Baxter and the Boost: splitting the difference

Abstract

In this paper we continue our classification of regular solutions of the Yang-Baxter equation using the method based on the spin chain boost operator developed in [1]. We provide details on how to find all non-difference form solutions and apply our method to spin chains with local Hilbert space of dimensions two, three and four. We classify all 16\times1616×16 solutions which exhibit \mathfrak{su}(2)\oplus \mathfrak{su}(2)𝔰𝔲(2)⊕𝔰𝔲(2) symmetry, which include the one-dimensional Hubbard model and the SS-matrix of the {AdS}_5 \times {S}^5AdS5×S5 superstring sigma model. In all cases we find interesting novel solutions of the Yang-Baxter equation.

Lifting integrable models and long-range interactions

“…Of course this is a case that was already classified in [3,4] and it is illustrative to compare the results. The Hamiltonian (3.8) is of type 6-vertex B and the corresponding R-matrix depends on several free functions.…”

“…We show that all known integrable long-range deformations of the 6-vertex models of this type can be obtained from a Lax operator and an R-matrix. Finally we discuss what happens at higher loops and highlight some general structures that these models seem to exhibit.Recently, we have started a research direction that focuses on the classification of regular solutions of the quantum Yang-Baxter equation [1,2,3,4,5]. However, from a practical point of view, using our classification to decide whether a Hamiltonian is integrable and descends from an R-matrix is not always very practical.…”

“…Recently, we have started a research direction that focuses on the classification of regular solutions of the quantum Yang-Baxter equation [1,2,3,4,5]. However, from a practical point of view, using our classification to decide whether a Hamiltonian is integrable and descends from an R-matrix is not always very practical.…”

Automorphic symmetries and $ AdS_n $ integrable deformations

“…Hence novel integrable solutions appear to be of non-difference form that admit AdS 2 and AdS 3 S-matrices as special cases, we also obtain embedding of double deformed sigma model R-matrix into one of the solutions. The braiding and crossing for the found models as well as their emergence with respect to the deformation parameter k are shown.The present contribution to proceedings is based on series of works [21,25,23,27] relevant to the questions discussed below.…”

“…The present contribution to proceedings is based on series of works [21,25,23,27] relevant to the questions discussed below.…”