量子可积系统理论在研究冷原子，自旋流体和电子关联系统的多体效应方面一直起到至关重要的作用。本研究项目的目的是应用杨-Baxter精确可解模型来研究低维超冷原子和自旋系统中的普适规律。基于冷原子气体最新的进展，拟开展以下几方面的工作: 1）用可测量的Wilson系数来研究一维吸引势下的自旋费米体系的新奇量子态和普适规律；2）研究高自旋费米和波色体系的量子临界现象，普适标度函数和关联函数；3）研究一维超冷原子多体散射问题中的杨－Baxter可积性，即非衍射性与衍射性多体散射的本质区别。这些研究结果将丰富和深化我们对冷原子和凝聚态物理中的量子多体问题的理解并对低维超冷原子实验具有实际的指导意义。

Quantum integrable systems have been playing a significant role in the study of many-body phenomena in cold atoms, spin liquids and correlated electrons.This project aims to apply Yang-Baxter exactly solvable models to understand universal quantum phenomena in ultracold atoms and spin liquids. In view of new developments of ultracold atoms, it will investigate 1) the measurable Wilson ratio for novel quantum states and universal many-body phenomena in one-dimensioanl spin fermionic systems with attactive interactions; 2) quantum criticality, universal scaling functions and correlation functions for low-dimensional large spin fermionic and bosonic systems; 3) the possibility of direct tests of Yang-Baxter integrability, i.e. the nature of non-diffractive and diffractive many-body scatterings in many-body systems. The results obtained will advance our fundamental knowledge in ultracold atoms and condensed matter physics, and thus help current experimental developments in these fields.