论文标题
Lieb-Schultz-Mattis，Luttinger和'T Hooft-晶格系统中的异常匹配
Lieb-Schultz-Mattis, Luttinger, and 't Hooft -- anomaly matching in lattice systems
论文作者
论文摘要
我们分析了晶格汉密尔顿系统的全球对称性具有hooft异常。正如在异常研究中常见的那样，它们是通过将系统耦合到经典背景计字段来探测的。对于平面场（消失的场强），可以将仪表场的非零空间组件视为扭曲的边界条件，也可以等效地将其视为拓扑缺陷。扭曲的希尔伯特空间的对称性及其表示捕获了异常。我们用许多示例演示了这种方法。在其中一些中，异常的对称性是晶格系统的内部对称性，但它们不在现场。 （我们阐明了“现场作用”的概念。）在其他情况下，异常的对称性涉及晶格翻译。使用这种方法，我们以统一的方式构建了许多已知和新的结果。在这项工作中，我们将自己局限于具有空间晶格的1+1D系统。特别是，我们提出了一个晶格系统，该晶格系统以任何半径（无BKT过渡）流向$ C = 1 $紧凑型玻色子系统，具有连续理论的完整内部对称性，其异常和t-二维。作为另一个应用程序，我们分析了各种自旋链模型，并将其lieb-shultz-mattis定理称为“ thooft异常匹配条件”。我们还展示了诸如luttinger定理等有意义的填充约束，也不能被视为反映异常。作为一种副产品，我们的理解使我们能够利用连续理论中的信息来得出一些确切的结果，例如感兴趣的晶格模型，例如低能量状态的晶格动量。
We analyze lattice Hamiltonian systems whose global symmetries have 't Hooft anomalies. As is common in the study of anomalies, they are probed by coupling the system to classical background gauge fields. For flat fields (vanishing field strength), the nonzero spatial components of the gauge fields can be thought of as twisted boundary conditions, or equivalently, as topological defects. The symmetries of the twisted Hilbert space and their representations capture the anomalies. We demonstrate this approach with a number of examples. In some of them, the anomalous symmetries are internal symmetries of the lattice system, but they do not act on-site. (We clarify the notion of "on-site action.") In other cases, the anomalous symmetries involve lattice translations. Using this approach we frame many known and new results in a unified fashion. In this work, we limit ourselves to 1+1d systems with a spatial lattice. In particular, we present a lattice system that flows to the $c=1$ compact boson system with any radius (no BKT transition) with the full internal symmetry of the continuum theory, with its anomalies and its T-duality. As another application, we analyze various spin chain models and phrase their Lieb-Shultz-Mattis theorem as an 't Hooft anomaly matching condition. We also show in what sense filling constraints like Luttinger theorem can and cannot be viewed as reflecting an anomaly. As a by-product, our understanding allows us to use information from the continuum theory to derive some exact results in lattice model of interest, such as the lattice momenta of the low-energy states.
