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Twist Deformations of Quantum Integrable Spin Chains

Dimitrijevic, Marija ; Lizzi, Fedele ; Kulish, Petr ; Wess, Julius ; Aschieri, Paolo

Noncommutative Spacetimes, 2009, Vol.774, p.167-190 [Periódico revisado por pares]

Germany: Springer Berlin / Heidelberg

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  • Título:
    Twist Deformations of Quantum Integrable Spin Chains
  • Autor: Dimitrijevic, Marija ; Lizzi, Fedele ; Kulish, Petr ; Wess, Julius ; Aschieri, Paolo
  • Assuntos: Bethe Equation ; Hopf Algebra ; Monodromy Matrix ; Quantum Group ; Spin Chain
  • É parte de: Noncommutative Spacetimes, 2009, Vol.774, p.167-190
  • Descrição: Twist deformations of spacetime lead to deformed field theories with twisted symmetries. Twisted symmetries are quantum group symmetries. Most integrable spin systems have dynamical symmetries related to appropriate quantum groups. We discuss the changes of the properties of these systems under twist transformations of quantum groups. A main example is the isotropic Heisenberg spin chain and the jordanian twist of the universal enveloping algebra of\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} l(2) end{document}. It is shown that the spectrum of the XXX label XXX model spin chain is preserved under the twist deformation while the structure of the eigenstates depends on the choice of boundary conditions. Another example is provided by abelian twists, these give physical deformations of closed spin chains corresponding to higher rank Lie algebras, e.g., \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} l(n) end{document}. The energy spectrum of these integrable models is changed and correspondingly their eigenvectors.
  • Títulos relacionados: Lecture Notes in Physics
  • Editor: Germany: Springer Berlin / Heidelberg
  • Idioma: Inglês
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