Abstract. We show that every regular Bethe ansatz eigenvector of the XXZ spin chain at roots of unity is a highest weight vector of the sl2 loop algebra, for some restricted sectors with respect to eigenvalues of the total spin operator S , and evaluate explicitly the highest weight in terms of the Bethe roots. We also discuss whether a given regular Bethe state in the sectors generates an irre...

This paper reviews the Bethe/gauge correspondence and its relation with geometric representation theory. The Bethe/gauge correspondence, first introduced by Nekrasov and Shatashvili, connects an N = (2, 2) supersymmetric gauge theory in two dimensions with an integrable system solvable by the Bethe ansatz. Both sides of the correspondence are discussed and then the Bethe/gauge correspondence is...

We show that every regular Bethe ansatz eigenstate of the XXZ spin chain at roots of unity is a highest weight vector of the sl2 loop algebra and discuss whether it generates an irreducible representation or not. We show it in some sectors with respect to eigenvalues of the total spin operator SZ . The parameter q is given by a root of unity, q2N 0 = 1, for an integer N . Here, q is related to ...

We study spin systems on Bethe lattices constructed from ddimensional hypercubes. Although these lattices are not tree-like, and therefore closer to real cubic lattices than Bethe lattices or regular random graphs, one can still use the Bethe-Peierls method to derive exact equations for the magnetization and other thermodynamic quantities. We compute phase diagrams for ferromagnetic Ising model...

We reformulate the nested coordinate Bethe ansatz in terms of coproducts of Yangian symmetry generators. This allows us to derive the nested Bethe equations for the bound state string S-matrices. We find that they coincide with the Bethe equations obtained from a fusion procedure. The bound state number dependence in the Bethe equations appears through the parameters x± and the dressing phase o...

In this thesis, new generalizations of the Bethe approximation and new understanding of the replica method are proposed. The Bethe approximation is an efficient approximation for graphical models, which gives an asymptotically accurate estimate of the partition function for many graphical models. The Bethe approximation explains the well-known message passing algorithm, belief propagation, whic...

in this study, chemical composition, fatty acid (fa) profile and oil characteristics of seeds of salvia leriifolia benht collected from different regions of iran. all samples were rich in oil (24-28.5% dry weight basis), protein (24.5-28.5%) and crude fiber (13.1-16.6%). the mean values for ca, p, k, mg, fe, mn, cu, na and zn were found at the levels of 3866, 2970, 3141, 2584, 57, 18.5, 9.0, 10...

We show that regular Bethe ansatz eigenvectors of the XXZ spin chain at roots of unity are highest weight vectors and generate irreducible representations of the sl2 loop algebra. We show it in some sectors with respect to eigenvalues of the total spin operator SZ . Here the parameter q, which is related to the XXZ anisotropy ∆ through ∆ = (q + q−1)/2, is given by a root of unity, q2N = 1, for ...

We show that regular Bethe ansatz eigenvectors of the XXZ spin chain at roots of unityare highest weight vectors and generate irreducible representations of the sl2 loop algebra.Here the parameter q, which is related to the XXZ anisotropy ∆ through ∆ = (q+q−1)/2,is given by a root of unity, q2N = 1, for an integer N . First, for a regular Bethe stateat a root of unity, we sh...