U(1)对称破缺量子可积系统的精确解是数学物理领域几十年来的著名遗留难题，在凝聚态物理、统计物理和高能理论物理都具有重要的应用。这类系统因缺乏参考态而使得传统的理论方法无法求解。本项目将充分发挥项目组在求解量子可积系统的方法方向上的优势，结合量子多体理论、超对称规范/弦理论、统计物理的结果，发展和完善求解一般U(1)对称破缺量子可积模型的本征值和本征态的方法，通过对一些典型对称破缺模型进行系统深入地研究，利用所得到的精确解研究相关物理体系的动力学行为，并积极探索它们在量子调控和超对称规范理论中应用，为理解U(1)对称破缺物理系统物理图像和机理提供理论指导。

Exact solutions of quantum integrable systems with U(1)-symmetry-broken, which have important applications in the condensed matter physics, the statistical physics and the theory of the high energy physics, have been challenged experts in the field for many years. Due to absence of an obvious reference state, the conventional Bethe ansatz methods cannot be applied to these kind models. The project will take the advantage of our new developed off-diagonal Bethe ansatz method and our plenty of experience on the conventional Bethe ansatz methods, and develop a novel, systemic and universal method to solve general integrable models associated with other non-A-type algebras. Through the systemic and detailed studies of the typical U(1)-symmetry-broken integrable models and their exact solutions, we hope to find some important physical mechanism and physical pictures, deepen the understanding of the many-body effects and promote the applications in quantum control and the supersymmetry quantum gauge theory.