Rational indices for quantum ground state sectors
Rational indices for quantum ground state sectors
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DOI：
10.1063/5.0021511
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发表时间：
2021-01-01
影响因子：
1.3
通讯作者：
Fraas, Martin
中科院分区：
文献类型：
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作者：
Bachmann, Sven;Bols, Alex;Fraas, Martin
我们考虑多体系统与有限简并的有空隙的基态子空间相互作用的电荷输运。对于任何保持局域性、电荷守恒的保持基态空间的酉性，我们关联一个是1/p的整数倍的指数，其中p是基态简并。我们证明了该指标在单位合成下是可加的。这种形式产生了几个应用：分数量子霍尔电导，分数Lieb-Schultz-Mattis(LSM)定理，它将标准LSM推广到平移不变性被打破的系统，以及Avron-Dana-Zak关系的相互作用推广。
We consider charge transport for interacting many-body systems with a gapped ground state subspace that 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 (LSM) 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 the Hall conductance and the filling factor.