非平行边界场下具有正交对称以及辛对称的可积量子自旋链的求解

具有正交对称以及辛对称的可积量子自旋链模型（即Bn、Dn和Cn模型）在凝聚态物理中有着重要的应用。为了更好地研究模型的边界磁场问题、掺杂效应，需要获得模型在非平行反射边界场下的严格解。由于这些模型的代数结构复杂，一直是严格解工作中的难点。非对角Bethe ansatz 方法是目前最具普适性的一种获得严格解的数学工具，但其核心组成部分-算子恒等式构成的封闭关系对于Bn、Dn和Cn模型来说现今依然未知，而非平行反射边界场的存在又给模型T-Q关系的构造增加了难度。因此，求解这些模型是一项具有挑战性且有意义的工作。目前，我们已经开展了这方面的一些工作，在国际上处于该领域中的领先地位。我们将通过在非平行反射边界场下对具有正交对称以及辛对称的可积量子自旋链模型的严格求解，完善和发展求解可解模型的理论框架，并完成高秩模型在非平行反射边界场下的求解和热力学计算，为在不同领域更广泛的应用打下良好的基础。

Exact solutions can provide a good visual angle in studying the low dimensional quantum many body systems, especially for those with strongly correlated interactions. Of all methods in dealing with exact solutions, Off-diagonal Bethe ansatz (ODBA) is the most powerful tool at present. The ODBA requires that its operator identities is close. How to find the closed operator identities is a tough work, especially for those systems with complex symmetry. Furthermore, when the system is in an unparallel boundary fields, the T-Q relations will become more complicated. The spin chains with orthogonal and symplectic symmetry (corresponding to the Bn,Dn and Cn vertex models) are important spin chain models in condensed matter physics, whose closed operator identities still remains unknown. It is a challenge to solve such models with the help of ODBA. We have carried out some work on the exact solutions for the spin chains with orthogonal and symplectic symmetry under unparallel boundary fields. It shows that closed operator identities are very different from those of the known SU(n) spin chain. Additionally, the T-Q relations can not be constructed yet when the boundary matrix are more generic. Here we will use ODBA to solve the Bn,Dn and Cn models with unparallel boundary fields and calculate their thermodynamic quantities for their possible applications.