Hierarchy of 1D Electron Models with Long-Range Interaction
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 . 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 , the OSp(N, 1) supersymmetric t-J model , a new hierarchy related to the edge states of the FQHE with the filling fraction v = 1/(p 1 − 1/ p2 −…− 1/ pN ) .
KeywordsSpin Chain Edge State Quantum Model Cartan Matrix Fractional Quantum Hall Effect
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