Author
E. K. Sklyanin
Bio: E. K. Sklyanin is an academic researcher from Steklov Mathematical Institute. The author has contributed to research in topics: Supersymmetry & Thirring model. The author has an hindex of 1, co-authored 1 publications receiving 744 citations.
Papers
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763 citations
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24 Sep 1987
TL;DR: The quantum inverse scattering method for solving nonlinear equations of evolution, the quantum theory of magnets, the method of commuting transfer-matrices in classical statistical mechanics, and factorizable scattering theory as discussed by the authors emerged as a natural development of the various directions in mathematical physics.
Abstract: Publisher Summary
This chapter focuses on the quantization of lie groups and lie algebras. The Algebraic Bethe Ansatz—the quantum inverse scattering method—emerges as a natural development of the various directions in mathematical physics: the inverse scattering method for solving nonlinear equations of evolution, the quantum theory of magnets, the method of commuting transfer-matrices in classical statistical mechanics, and factorizable scattering theory. The chapter discusses quantum formal groups, a finite-dimensional example, an infinite-dimensional example, and reviews the deformation theory and quantum groups.
1,584 citations
TL;DR: The first rigorous example of an isotropic model in such a phase is presented in this paper, where the Hamiltonian has an exactSO(3) symmetry and is translationally invariant, but the model has a unique ground state and exponential decay of the correlation functions in the ground state.
Abstract: Haldane predicted that the isotropic quantum Heisenberg spin chain is in a “massive” phase if the spin is integral. The first rigorous example of an isotropic model in such a phase is presented. The Hamiltonian has an exactSO(3) symmetry and is translationally invariant, but we prove the model has a unique ground state, a gap in the spectrum of the Hamiltonian immediately above the ground state and exponential decay of the correlation functions in the ground state. Models in two and higher dimension which are expected to have the same properties are also presented. For these models we construct an exact ground state, and for some of them we prove that the two-point function decays exponentially in this ground state. In all these models exact ground states are constructed by using valence bonds.
1,105 citations
TL;DR: In this article, a review of quantum integrable finite-dimensional systems related to Lie algebras is presented, which contains results such as the forms of spectra, wave functions, S-matrices and quantum integrals of motion.
1,007 citations
728 citations
Book•
30 Oct 2007TL;DR: The quantum determinant and the Sklyanin determinant of block matrices have been studied in this paper, where the quantum contraction and the quantum Liouville formula for the twisted Yangian are presented.
Abstract: Contents §0. Introduction §1. The Yangian §2. The quantum determinant and the centre of §3. The twisted Yangian §4. The Sklyanin determinant and the centre of §5. The quantum contraction and the quantum Liouville formula for the Yangian §6. The quantum contraction and the quantum Liouville formula for the twisted Yangian §7. The quantum determinant and the Sklyanin determinant of block matrices Bibliography
550 citations