论文标题
迈向广义ISING模型的不可变形异常
Towards Non-Invertible Anomalies from Generalized Ising Models
论文作者
论文摘要
我们提出了一种一般方法，以实现不可理性拓扑阶段的宽大对应关系，包括拓扑和分形式顺序。这是通过一种新颖的批量构造协议来实现的，在该协议中，可解的$（D+1）$ - 具有不可拓扑拓扑的尺寸散装模型是由$ D $ dimensions中所谓的广义ising（GI）模型构建的。然后，GI模型可以终止在批量模型的边界上。该结构生成了丰富的示例，不仅包括任何尺寸的原型示例，例如$ z_2 $ toric代码模型，以及X-Cube Fracton模型，还包括$ Z_2 \ Z2 \ times Z_2 $拓扑顺序，诸如4D $ Z_2 $ tosoliend of Solige of Solity Solvery Sons的范围，以及X-Cube fracton模型，诸如$ Z_2 \ times z_2 $ times z_2 $ topogical Order和spections。具有某些总体对称性电荷和/或满足某些边界条件的GI模型。我们得出了这种散装边界对应关系的具体条件。只有在散装模型是微不足道或分裂有序的情况下，就会违反这种情况。 Kramers-Wannier二重性的广义概念在建筑中起着重要作用。同样，利用二元性，我们找到了一个示例，即可以在两个不同的散装法族人模型的边界上实现单个异常理论，这是在拓扑顺序的情况下预期的现象。更一般而言，拓扑订单也可以从GI模型以外的晶格模型开始，例如具有对称性受保护的拓扑订单的晶格模型，这是通过变异的散装结构，我们在附录中提供。
We present a general approach to the bulk-boundary correspondence of noninvertible topological phases, including both topological and fracton orders. This is achieved by a novel bulk construction protocol where solvable $(d+1)$-dimensional bulk models with noninvertible topology are constructed from the so-called generalized Ising (GI) models in $d$ dimensions. The GI models can then terminate on the boundaries of the bulk models. The construction generates abundant examples, including not only prototype ones such as $Z_2$ toric code models in any dimensions no less than two, and the X-cube fracton model, but also more diverse ones such as the $Z_2\times Z_2$ topological order, the 4d $Z_2$ topological order with pure-loop excitations, etc. The boundary of the solvable model is potentially anomalous and corresponds to precisely only sectors of the GI model that host certain total symmetry charges and/or satisfy certain boundary conditions. We derive a concrete condition for such bulk-boundary correspondence. The condition is violated only when the bulk model is either trivial or fracton ordered. A generalized notion of Kramers-Wannier duality plays an important role in the construction. Also, utilizing the duality, we find an example where a single anomalous theory can be realized on the boundaries of two distinct bulk fracton models, a phenomenon not expected in the case of topological orders. More generally, topological orders may also be generated starting with lattice models beyond the GI models, such as those with symmetry protected topological orders, through a variant bulk construction, which we provide in an appendix.
