Bootstrapping Lieb-Schultz-Mattis anomalies
Bootstrapping Lieb-Schultz-Mattis anomalies
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DOI：
10.1103/physrevb.107.205137
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发表时间：
2022-07
影响因子：
3.7
通讯作者：
Ryan A. Lanzetta;L. Fidkowski
中科院分区：
文献类型：
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作者：
Ryan A. Lanzetta;L. Fidkowski
我们将导致一维自旋链的 Lieb-Schultz-Mattis (LSM) 定理一定推广的微观假设纳入共形自举中。我们的方法通过对称缺陷算子的模块化自举和相关自举的组合来解释这些自旋链所具有的“LSM异常”。因此，我们获得了 (1+1)$d$ 共形场论 (CFT) 局部算子内容的通用界限，该理论可以用在每个位置投影实现的 $\mathbb Z_N\times \mathbb Z_N$ 对称性来描述平移不变格子哈密顿量。我们提出了局部算子的界限，无论是否通过其全局对称表示进行细化。有趣的是，当 $N$ 为奇数时，我们可以获得带电运算符的非平凡界限，而事实证明，仅使用模块化引导程序是不可能的。我们的界限表现出独特的怪癖，其中一些几乎被已知的理论所饱和，而另一些则无法解释。我们讨论了其他场景以及我们的边界应用所需的属性，包括 (1+1)$d$ 对称保护拓扑相之间的某些多临界点，我们认为在我们的引导计算中研究的异常应该出现。
We incorporate the microscopic assumptions that lead to a certain generalization of the Lieb-Schultz-Mattis (LSM) theorem for one-dimensional spin chains into the conformal bootstrap. Our approach accounts for the"LSM anomaly"possessed by these spin chains through a combination of modular bootstrap and correlator bootstrap of symmetry defect operators. We thus obtain universal bounds on the local operator content of (1+1)$d$ conformal field theories (CFTs) that could describe translationally invariant lattice Hamiltonians with a $\mathbb Z_N\times \mathbb Z_N$ symmetry realized projectively at each site. We present bounds on local operators both with and without refinement by their global symmetry representations. Interestingly, we can obtain non-trivial bounds on charged operators when $N$ is odd, which turns out to be impossible with modular bootstrap alone. Our bounds exhibit distinctive kinks, some of which are approximately saturated by known theories and others that are unexplained. We discuss additional scenarios with the properties necessary for our bounds to apply, including certain multicritical points between (1+1)$d$ symmetry protected topological phases, where we argue that the anomaly studied in our bootstrap calculations should emerge.