Exactly solvable model for a 4+1D beyond-cohomology symmetry-protected topological phase
Exactly solvable model for a 4+1D beyond-cohomology symmetry-protected topological phase
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DOI：
10.1103/physrevb.101.155124
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发表时间：
2019-12
影响因子：
3.7
通讯作者：
L. Fidkowski;Jeongwan Haah;M. Hastings
中科院分区：
文献类型：
--
作者：
L. Fidkowski;Jeongwan Haah;M. Hastings
我们为 ($4+1$) 维 ${\mathbb{Z}}_{2}$ 对称保护拓扑相 (SPT) 构建了一个完全可解的通勤投影模型，该拓扑相位于 SPT 的上同调分类之外。该模型由装饰域壁结构描述，域壁上具有“三费米子”Walker-Wang 相。我们以多种方式描述该相的异常性质。一个有趣的特征是，与上同调相相比，($3+1$) 维边界上的有效 ${\mathbb{Z}}_{2}$ 对称性不能用量子电路来描述，而是一个不平凡的量子元胞自动机。一个相关的性质是余维二缺陷（例如，${\mathbb{Z}}_{2}$畴壁在平凡边界处的终止）将携带非平凡的手性中心电荷4 mod 8。我们还为我们的模型构造了一个有间隙的对称拓扑有序边界态，它构成了Chen和Hermele分类之外的异常对称性丰富的拓扑相，并定义了相应的异常指示符。
We construct an exactly solvable commuting projector model for a ($4+1$)-dimensional ${\mathbb{Z}}_{2}$-symmetry-protected topological phase (SPT) which is outside the cohomology classification of SPTs. The model is described by a decorated domain wall construction, with ``three-fermion'' Walker-Wang phases on the domain walls. We describe the anomalous nature of the phase in several ways. One interesting feature is that, in contrast to in-cohomology phases, the effective ${\mathbb{Z}}_{2}$ symmetry on a ($3+1$)-dimensional boundary cannot be described by a quantum circuit and instead is a nontrivial quantum cellular automaton. A related property is that a codimension-two defect (for example, the termination of a ${\mathbb{Z}}_{2}$ domain wall at a trivial boundary) will carry nontrivial chiral central charge 4 mod 8. We also construct a gapped symmetric topologically ordered boundary state for our model, which constitutes an anomalous symmetry-enriched topological phase outside of the classification of Chen and Hermele, and define a corresponding anomaly indicator.