In this paper, we present a detailed analysis of the diagonalization of the higher spin Heisenberg model using its quantum affine symmetry $U_q(\hat{sl(2)})$ . In particular, we describe the bosonizations of the latter algebra, its highest weight representations, vertex operators and screening operators. Finally, we use this bosonization method to compute the vacuum-to-vacuum expectation values and the form factors of any local operator.In this paper, we present a detailed analysis of the diagonalization of the higher spin Heisenberg model using its quantum affine symmetry $U_q(\hat{sl(2)})$. In particular, we describe the bosonizations of the latter algebra, its highest weight representations, vertex operators and screening operators. Finally, we use this bosonization method to compute the vacuum-to-vacuum expectation values and the form factors of any local operator.

arXiv:q-alg/9706015Jun 14, 19979 citations

Quantum Affine Symmetry and Correlation Functions of the XXZ Model

Tetsuji Miwa

NATO ASI series. Series B : PhysicsJan 1, 19930 citations

Fractional spin through quantum affine algebras

Mostafa Mansour, E. H. Zakkari

Mar 25, 20030 citations

Drinfel'd Twists and Algebraic Bethe Ansatz

Jean Michel Maillet, J.M. Sánchez de Santos

We study representation theory of Drinfel'd twists, in terms of what we call F matrices, associated to finite dimensional irreducible modules of quantum affine algebras, and which factorize the corresponding (unitary) R matrices. We construct explicitly such factorizing F matrices for irreducible tensor products of the fundamental representations of the quantum affine algebra sl2 and its associated Yangian. We then apply these constructions to the XXX and XXZ quantum spins chains of finite length in the framework of the Algebraic Bethe Ansatz.We study representation theory of Drinfel'd twists, in terms of what we call F matrices, associated to finite dimensional irreducible modules of quantum affine algebras, and which factorize the corresponding (unitary) R matrices. We construct explicitly such factorizing F matrices for irreducible tensor products of the fundamental representations of the quantum affine algebra sl2 and its associated Yangian. We then apply these constructions to the XXX and XXZ quantum spins chains of finite length in the framework of the Algebraic Bethe Ansatz.

arXiv:q-alg/9612012Dec 10, 19962 citations

In this paper, we present a detailed analysis of the diagonalization of the higher spin Heisenberg model using its quantum affine symmetry

U_q(\hat{sl(2)})

. In particular, we describe the bosonizations of the latter algebra, its highest weight representations, vertex operators and screening operators. Finally, we use this bosonization method to compute the vacuum-to-vacuum expectation values and the form factors of any local operator.