arXiv subjects
Publications and source records attributed to Kang Xue.
A unified treatment is developed for the XXX-Heisenberg model and a long-ranged interaction model (the $H_2$ in Haldane-Shastry model) from the point of view of shift operators (or raising and lowering operators), based on which the energy spectra of the spin-chain models are determined. Some physical discussions are also made.
The shift operators for XXX-Heisenberg chain are found. They are formed by local Yangian operators and the amplitutes of the eigenfunctions obeying Bethe ansatz for the Hamiltonian. The physical implication of the shift operators are also explained.
This is an introduction to the physical pictures of {\em Yangian} symmetry. All the discussions are based on the RTT relations which have been known to be related to the Hamiltonian formulations for quantum integrable systems. The explicit calculations of {\em Yangian} associated with $gl(2)$ are given through solving the RTT relations. It contains the Drinfeld's $Y(sl(2))$, $Y(sl(n))$ and Heisenberg type of Hopf algebras. Examples are emphasized to show the physical pictures, such as Hubbard model, Haldane-Shastry model, Long-range interaction models and Goryachev-Chaplygin(G-C) gyrostat. The example of the trigonometric extension of G-C gyrostat are also shown that leads to the non-commutative geometry naturally on the basis of the truncated $q$-affine algebra.