Yangian symmetry of integrable quantum chains with long-range interactions and a new description of states in conformal field theory

1992/10/05 by F. D. M. Haldane, Zou Ha, J. C. Talstra +2 · 10 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #Nonlinear Photonic Systems #Yangian #Physics #Conformal field theory #Quantum inverse scattering method #Mathematical physics #Quantum field theory #Conformal symmetry #Symmetry (geometry) #Bosonization #Crossing #Quantum mechanics #Field (mathematics) #Conformal map #Quantum #Theoretical physics #S-matrix #Pure mathematics #Scattering theory #Mathematics #Scattering #Fermion

paper · doi:10.1103/physrevlett.69.2021

openalex publication_date 1992/10/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/02

Abstract

The SU(n) quantum chains with inverse-square exchange exhibit a novel form of Yangian symmetry compatible with periodic boundary conditions, allowing states to be countable. We characterize the ``supermultiplets'' of the spectrum in terms of generalized ``occupation numbers.'' We embed the model in the k=1 SU(n) Kac-Moody algebra and obtain a new classification of the states of conformal field theory, adapted to particlelike elementary excitations obeying fractional statistics.

Citations

• THE QUANTUM METHOD OF THE INVERSE PROBLEM AND THE HEISENBERG XYZ MODEL

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