论文标题
在三个空间维度中解开超级酒精学对称性保护拓扑阶段
Disentangling supercohomology symmetry-protected topological phases in three spatial dimensions
论文作者
论文摘要
我们在（3+1）d分类的（3+1）d分类的（3+1）d中构建了可解决的晶格哈密顿量。我们结构的一个核心优势是它产生明确的有限深度量子电路（FDQC），该电路从未进入的对称状态中制备了基态。 FDQC使我们能够清楚地证明超级酒精学阶段的特征性能 - 即，对Fermion Prux通路环的对称分数 - 通过连续公式预测。通过组成相应的FDQC，我们还恢复了超级酒精学阶段的堆叠关系。此外，我们通过扩展保护对称性来得出超级酒精学模型的拓扑排序的边界，这类似于造型的玻色粒SPT阶段的拓扑排序边界。我们的方法在很大程度上依赖于将某些玻色粒2组SPT相与超级酒精学SPT阶段相关联的二元性。我们从二元处方的方面发展了二元性的物理动机，以测量一种1形式对称性和凝结紧急费米子。我们还评论了在高维度和超级酒精学框架之外对超级酒精学阶段的概括。
We build exactly solvable lattice Hamiltonians for fermionic symmetry-protected topological (SPT) phases in (3+1)D classified by group supercohomology. A central benefit of our construction is that it produces an explicit finite-depth quantum circuit (FDQC) that prepares the ground state from an unentangled symmetric state. The FDQC allows us to clearly demonstrate the characteristic properties of supercohomology phases - namely, symmetry fractionalization on fermion parity flux loops - predicted by continuum formulations. By composing the corresponding FDQCs, we also recover the stacking relations of supercohomology phases. Furthermore, we derive topologically ordered gapped boundaries for the supercohomology models by extending the protecting symmetries, analogous to the construction of topologically ordered boundaries for bosonic SPT phases. Our approach relies heavily on dualities that relate certain bosonic 2-group SPT phases with supercohomology SPT phases. We develop physical motivation for the dualities in terms of explicit lattice prescriptions for gauging a 1-form symmetry and for condensing emergent fermions. We also comment on generalizations to supercohomology phases in higher dimensions and to fermionic SPT phases outside of the supercohomology framework.
