论文标题
量子晶格系统和间隙状态的拓扑不变的本地定理
Local Noether theorem for quantum lattice systems and topological invariants of gapped states
论文作者
论文摘要
我们研究了任意维度量子晶格系统的浆果阶段的概括。对于在d维度中平稳的基础状态的平滑家族，我们在参数空间上定义了一个封闭的（d+2） - 概括浆果连接的曲率。它的共同学课是家庭的拓扑不变。当家族在紧凑的谎言组G的作用下是均等的时，拓扑不变性在参数空间的模棱两可的共同体中。这些不变的人统一并概括了大厅的电导和无与伦比的泵。在这些构造中的关键作用是由附在任何量子晶格系统上的某个差分级的特定型莱型代数发挥的。作为一种副产品，我们描述了具有迅速衰减相互作用的任意晶格系统的电荷密度和保守电流的歧义。
We study generalizations of the Berry phase for quantum lattice systems in arbitrary dimensions. For a smooth family of gapped ground states in d dimensions, we define a closed (d+2)-form on the parameter space which generalizes the curvature of the Berry connection. Its cohomology class is a topological invariant of the family. When the family is equivariant under the action of a compact Lie group G, topological invariants take values in the equivariant cohomology of the parameter space. These invariants unify and generalize the Hall conductance and the Thouless pump. A key role in these constructions is played by a certain differential graded Frechet-Lie algebra attached to any quantum lattice system. As a by-product, we describe ambiguities in charge densities and conserved currents for arbitrary lattice systems with rapidly decaying interactions.
