XXZ模型的Bethe Ansatz解与量子群的最高权态

Bethe Ansatz Solutions of XXZ Model and Highest Weight States of Quantum Group

一维Heisenberg开链的XXZ模型有量子群SUq(2)的对称性,本文证明能量本征值方程的Bethe Ansatz解是SUq(2)的最高权态,并说明Bethe Ansatz解中的impulsion k可取得使e^(ik)=q。

It's been proved that for the XXX model with fixed boundary conditions, Bethe Ansatz states are correspondingly the highest weight states of SU(2). The anisotropic XXZ model no longer enjoys SU(2) symmetry but rather has quantum group symmetry SU_q(2). We explicitly prove that Bethe Ansatz States arethe highest weight states of SU_(q)(2). And contrary to the claims by Pasquier and Saleur, we argue that the impulsion kcan be chosen so that e^(ik) =q.