Generalized Boundary Condition Applied to Lieb-Schultz-Mattis-Type Ingappabilities and Many-Body Chern Numbers
Generalized Boundary Condition Applied to Lieb-Schultz-Mattis-Type Ingappabilities and Many-Body Chern Numbers
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DOI：
10.1103/physrevx.10.031008
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发表时间：
2019-06
影响因子：
12.5
通讯作者：
Yuan Yao;M. Oshikawa
中科院分区：
文献类型：
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作者：
Yuan Yao;M. Oshikawa
我们引入了一个新的边界条件，使得二维或更高维Lieb-Schultz-Mattis定理的通量插入变元不受系统大小的具体选择。它还使任意维上的Lieb-Schultz-Mattis型定理可以用1+1$维场论中的反常形式来表述，它与2+1维上的BF理论具有整体对应关系。此外，利用时间反转、磁平移和现场内部的$U(N)对称性，我们将基于反常的公式应用于正方形晶格上具有$\pi$通量的半充满的无自旋费米子的约束。这证明了时间反转反常对格子模型的不可应用性的作用。
We introduce a new boundary condition which renders the flux-insertion argument for the Lieb-Schultz-Mattis type theorems in two or higher dimensions free from the specific choice of system sizes. It also enables a formulation of the Lieb-Schultz-Mattis type theorems in arbitrary dimensions in terms of the anomaly in field theories of $1+1$ dimensions with a bulk correspondence as a BF-theory in 2+1 dimensions. Furthermore, we apply the anomaly-based formulation to the constraints on a half-filled spinless fermion on a square lattice with $\pi$ flux, utilizing time-reversal, the magnetic translation and on-site internal $U(N)$ symmetries. This demonstrates the role of time-reversal anomaly on the ingappabilities of a lattice model.