凝聚态物理中的规范不变性与反常
Gauge Invariance and Anomalies in Condensed Matter Physics
AI总结：
本文系统回顾了凝聚态物理中规范理论与手征反常的核心作用，涵盖量子线、量子霍尔效应、拓扑绝缘体、外尔半金属及轴子电动力学，并推导了陈-西蒙斯作用量与边缘反常作用量。
摘要：
本文首先总结了一种用于研究凝聚态物理中电子态的强大形式体系，称为“物质态/相的规范理论”。回顾了在该形式体系中扮演着相当重要角色的手征反常。随后，我概述了1+1维手征反常在一维量子线中的应用。接着，回顾了二维（2D）有能隙（“不可压缩”）电子液体中量子霍尔效应的若干要素。特别地，我讨论了在时间反演被显式或自发破缺的二维有能隙电子液体（即霍尔绝缘体和陈绝缘体）中，反常手征边缘电流和反常流入的作用。推导了给出此类系统体内部有效输运方程的拓扑陈-西蒙斯作用量以及相应的反常边缘作用量。概述了对“阿贝尔”霍尔绝缘体进行一般分类的结果。在对诱导陈-西蒙斯作用量作若干评述之后，我概述了关于某些二维手征光子波导的结果。然后，我继续分析具有自旋-轨道相互作用的电子气所构成的时间反演不变二维拓扑绝缘体中的手征边缘自旋流和体响应方程。接下来回顾了三维系统中的“手征磁效应”和轴子电动力学。这为概述包括“轴子绝缘体”在内的三维拓扑绝缘体一般理论奠定了基础。最后，对表现出手征磁效应的外尔半金属以及具有动力学类轴子自由度的三维系统中的莫特转变作了一些评述，以此结束本综述。
英文摘要：
This paper begins with a summary of a powerful formalism for the study of electronic states in condensed matter physics called "Gauge Theory of States/Phases of Matter." The chiral anomaly, which plays quite a prominent role in that formalism, is recalled. I then sketch an application of the chiral anomaly in 1+1 dimensions to quantum wires. Subsequently, some elements of the quantum Hall effect in two-dimensional (2D) gapped ("incompressible") electron liquids are reviewed. In particular, I discuss the role of anomalous chiral edge currents and of anomaly inflow in 2D gapped electron liquids with explicitly or spontaneously broken time reversal, i.e., in Hall- and Chern insulators. The topological Chern-Simons action yielding the transport equations valid in the bulk of such systems and the associated anomalous edge action are derived. The results of a general classification of "abelian" Hall insulators are outlined. After some remarks on induced Chern-Simons actions, I sketch results on certain 2D chiral photonic wave guides. I then continue with an analysis of chiral edge spin-currents and the bulk response equations in time-reversal invariant 2D topological insulators of electron gases with spin-orbit interactions. The "chiral magnetic effect" in 3D systems and axion-electrodynamics are reviewed next. This prepares the ground for an outline of a general theory of 3D topological insulators, including "axionic insulators". Some remarks on Weyl semi-metals, which exhibit the chiral magnetic effect, and on Mott transitions in 3D systems with dynamical axion-like degrees of freedom conclude this review.}
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