物质的绝缘态：几何理论
The Insulating State of Matter: A Geometrical Theory
摘要：
1964年W. Kohn发表了里程碑式的论文“绝缘态理论”，根据该理论，绝缘体和金属的基态不同。甚至在系统被任何探针激发之前，在基态中就存在不同的电子组织，这是区分绝缘体和金属的关键特征。然而，绝缘状态的理论仍然有些不完整，直到20世纪90年代末;这篇评论解决了最近的发展。任何绝缘体的多体基态波函数都可以用几何概念（贝里相位、连接、曲率、陈数、量子度规）来描述。其中，量子度规最能刻画物质的绝缘状态。该理论涉及几种绝缘体的共同点：带状绝缘体、莫特绝缘体、安德森绝缘体、量子霍尔绝缘体、陈氏绝缘体和拓扑绝缘体
英文摘要：
In 1964 W. Kohn published the milestone paper "Theory of the insulating state'", according to which insulators and metals differ in their ground state. Even before the system is excited by any probe, a different organization of the electrons is present in the ground state and this is the key feature discriminating between insulators and metals. However, the theory of the insulating state remained somewhat incomplete until the late 1990s; this review addresses the recent developments. The many-body ground wavefunction of any insulator is characterized by means of geometrical concepts (Berry phase, connection, curvature, Chern number, quantum metric). Among them, it is the quantum metric which sharply characterizes the insulating state of matter. The theory deals on a common ground with several kinds of insulators: band insulators, Mott insulators, Anderson insulators, quantum Hall insulators, Chern and topological insulators
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