论文标题
量子基态扇区的理性指数
Rational indices for quantum ground state sectors
论文作者
论文摘要
我们考虑将多体系统与基础状态子空间相互作用的电荷运输，该系统有限地退化且拓扑结构。对于保存基态空间的任何地方保存，支撑统一的统一，我们将一个索引与整数倍数相关联，该指数是$ 1/p $的整数倍数，其中$ p $是基础状态变性。我们证明该索引在单位组成下是加性。这种形式主义引起了几种应用：分数量子霍尔电导，这是一种分数lieb-schultz-mattis定理，该定理将标准LSM推广到破坏翻译不变性的系统，以及霍尔电导和填充因子之间的Avron-Dana-Zak关系的相互作用概括。
We consider charge transport for interacting many-body systems with a gapped ground state subspace which is finitely degenerate and topologically ordered. To any locality-preserving, charge-conserving unitary that preserves the ground state space, we associate an index that is an integer multiple of $1/p$, where $p$ is the ground state degeneracy. We prove that the index is additive under composition of unitaries. This formalism gives rise to several applications: fractional quantum Hall conductance, a fractional Lieb-Schultz-Mattis theorem that generalizes the standard LSM to systems where the translation-invariance is broken, and the interacting generalization of the Avron-Dana-Zak relation between Hall conductance and the filling factor.
