U(1)对称破缺超对称量子可积系统的精确量子化及关联函数

在量子可积领域内，存在一类与超代数相关的量子可积模型，它们广泛应用于AdS/CFT、强关联电子理论等理论中。具有U(1)对称性的这类模型利用传统的Bethe ansatz方法已被求解，但是随着拓扑物理和弦理论的发展，许多有趣的现象比如边缘态、Majorana零模和拓扑激发等被发现，使得这类超对称可积模型在非对角可积条件下的研究成为一个非常有趣的问题。本项目结合擅长的非对角Bethe ansatz方法和聚合思想，发展一套求解超对称量子可积模型的方法，通过对拓展的Hubbard模型和t-J模型这两个典型的超对称量子可积模型进行深入的研究，利用精确解的结果研究系统的热力性质和关联特性等，并探索U(1)对称性破缺所导致的新现象。

In the quantum integrable field, there exists a class of quantum integrable models related with superalgebra, which has many applications in AdS/CFT correspondence, strongly correlated electronic theory, etc. These models with U(1) symmetry has been solved by traditional Bethe ansatz method. But with the development of topological physics and string theory, many interesting phenomena such as edge states, Majorana zero modes and topological excitations have been found. That makes study on the supersymmetric quantum integrable with off-diagonal boundaries becomes a very interesting issue. The project will take our new developed off-diagonal Bethe ansatz method and fusion process, develop a systemic method to solve supersymmetric quantum integrable models. Through the detailed studies of the Hubbard model and t-J model and their exact solutions, we hope to find the thermodynamic property and correlation property and explore the new phenomenon caused by the U(1) symmetry broken.