Spinorial R operator and Algebraic Bethe Ansatz

  title={Spinorial R operator and Algebraic Bethe Ansatz},
  author={David Karakhanyan and Roland Kirschner},
  journal={Nuclear Physics B},


We study the class of o 2 n +1 -invariant quantum integrable models in the framework of the algebraic Bethe ansatz and propose a construction of the o 2 n +1 -invariant Bethe vector in terms of the

O ct 2 02 0 Representations of orthogonal and symplectic Yangians 1

Exteded Yangian algebras of orthogonal and symplectic types are defined by the YangBaxter RLL relation involving the fundamental R-matrix with so(n) or sp(2m) symmetry. We study representations of

Algebraic Bethe ansatz for $$\mathfrak o_{2n+1}$$ -invariant integrable models

Abstract We study the class of $$ \mathfrak{o} _{2n+1}$$ -invariant quantum integrable models in the framework of the algebraic Bethe ansatz and propose a construction of the $$ \mathfrak{o}

Algebraic Bethe Ansatz for spinor R-matrices

<jats:p>We present a supermatrix realisation of <jats:inline-formula><jats:alternatives><jats:tex-math>q</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"

Spinor Representations of Orthogonal and Symplectic Yangians

We consider the explicit spinor \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}



New symmetries of gl(N)-invariant Bethe vectors

We consider quantum integrable models solvable by the nested algebraic Bethe ansatz and possessing -invariant R-matrix. We study two types of Bethe vectors. The first type corresponds to the original

Algebraic Bethe Ansatz for SO(N)-invariant transfer matrices

A matrix version of an algebraic Bethe Ansatz is proposed for R-matrices of a special structure. It is shown that SO(N)-invariant R-matrices in spinor representation possess this special structure.

How algebraic Bethe ansatz works for integrable model

I study the technique of Algebraic Bethe Ansatz for solving integrable models and show how it works in detail on the simplest example of spin 1/2 XXX magnetic chain. Several other models are treated

The spinorial R-matrix

The R-matrix acting in the tensor product of two spinor representation spaces of Lie algebra so(d) is considered thoroughly. The corresponding Yang–Baxter relation is proved and the underlying local

Nested Bethe Ansatz for the RTT Algebra of sp(4) Type

We show how to formulate the algebraic nested Bethe ansatz for RTT algebras with an R-matrix of the sp(4) type. We obtain the Bethe vectors and Bethe conditions for any highest-weight representation

Local Hamiltonians for integrable quantum models on a lattice. II

This paper discusses a method of constructing local Hamiltonians for integrable lattice models proposed by Tarasov, Takhtadzhyan, and Faddeev. The method is generalized to the case of inhomogeneous

Integrable models of quantum one-dimensional magnets with O(n) and Sp(2k) symmetry

The authors investigate quantum models on a chain with O(n) and Sp(2k) symmetry. The eigenvalues of the corresponding transfer matrices on a finite lattice are calculated. A generalization of the

Equivalences between three presentations of orthogonal and symplectic Yangians

We prove the equivalence of two presentations of the Yangian $$Y(\mathfrak {g})$$Y(g) of a simple Lie algebra $$\mathfrak {g}$$g, and we also show the equivalence with a third presentation when