具有全局对称性的强关联拓扑物态的规范场论

Gauge theory of strongly-correlated symmetric topological Phases

在有对称性保护的条件下,拓扑能带绝缘体等自由费米子体系的拓扑不变量可以在能带结构计算中得到.但是,为了得到强关联拓扑物质态的拓扑不变量,我们需要全新的理论思路.最典型的例子就是分数量子霍尔效应:其低能有效物理一般可以用Chern-Simons拓扑规范场论来计算得到;霍尔电导的量子化平台蕴含着十分丰富的强关联物理.本文将讨论存在于玻色和自旋模型中的三大类强关联拓扑物质态:本征拓扑序、对称保护拓扑态和对称富化拓扑态.第一类无需考虑对称性,后两者需要考虑对称性.理论上,规范场论是一种非常有效的研究方法.本文将简要回顾用规范场论来研究强关联拓扑物质态的一些研究进展.具体内容集中在"投影构造理论"、"低能有效理论"、"拓扑响应理论"三个方面.

In the presence of symmetry-protection,topological invariants of topological phases of matter in free fermion systems,e.g.,topological band insulators,can be directly computed via the properties of band structure.Nevertheless,it is usually difficult to extract topological invariants in strongly-correlated topological phases of matter in which band structure is not well-defined.One typical example is the fractional quantum Hall effect whose low-energy physics is governed by Chern-Simons topological gauge theory and Hall conductivity plateaus involve extremely fruitful physics of strong correlation.In this article,we focus on intrinsic topological order(iTO),symmetry-protected topological phases(SPT),and symmetry-enriched topological phases(SET)in boson and spin systems.Through gauge field-theoretical approach,we review some research progress on these topological phases of matter from the aspects of projective construction,low-energy effective theory and topological response theory.