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Hierarchy of 1D Electron Models with Long-Range Interaction

  • Norio Kawakami
Part of the NATO ASI Series book series (NSSB, volume 343)

Abstract

One-dimensional (1D) quantum models with 1/r 2 interaction have been studied extensively in connection with basic concepts in condensed matter physics such as the random matrix, the fractional quantum Hall effect (FQHE), etc [1–13]. Besides much interest in the integrability, the above class of quantum models involve interesting applications to highly correlated electron systems. The asymptotic Bethe ansatz solution (ABA) provides us with a systematic way to treat bulk quantities as well as excitation spectra [2]. We have obtained the ABA solution systematically to hierarchical families of quantum models with 1/r 2 interaction, such as the SU(N) Haldane-Shastry spin chain [8], the OSp(N, 1) supersymmetric t-J model [8], a new hierarchy related to the edge states of the FQHE with the filling fraction v = 1/(p 1 − 1/ p2 −…− 1/ pN ) [13].

Keywords

Spin Chain Edge State Quantum Model Cartan Matrix Fractional Quantum Hall Effect 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • Norio Kawakami
    • 1
  1. 1.Yukawa Institute for Theoretical PhysicsKyoto UniversityKyoto 606Japan

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