标题： 陈-西蒙斯理论在自旋链上的编码 显示英文标题

标题： Chern-Simons theory encoded on a spin chain

摘要： 我们构建了一个具有通用相互作用的一维自旋链哈密顿量，并证明该模型的热关联函数可以显式地用随机矩阵表示。 作为该结果的应用，我们展示了如何通过一维自旋链（XX型）的热关联函数，在选择适当的指数衰减相互作用与无限多邻居之间的情况下，再现$U(N)$陈-西蒙斯理论在$S^{3}$上的可观测量。 我们证明对于该模型，有限温度$\beta =1$下自旋链的关联函数给出了陈-西蒙斯划分函数、量子维度以及完整的拓扑$S$矩阵。 显示英文摘要

摘要： We construct a 1d spin chain Hamiltonian with generic interactions and prove that the thermal correlation functions of the model admit an explicit random matrix representation. As an application of the result, we show how the observables of $U(N)$ Chern-Simons theory on $S^{3}$ can be reproduced with the thermal correlation functions of the 1d spin chain, which is of the XX type, with a suitable choice of exponentially decaying interactions between infinitely many neighbours. We show that for this model, the correlation functions of the spin chain at a finite temperature $\beta =1$ give the Chern-Simons partition function, quantum dimensions and the full topological $S$-matrix.