Floquet gap-dependent topological classifications from color-decorated frequency lattices with space-time symmetries
Floquet gap-dependent topological classifications from color-decorated frequency lattices with space-time symmetries
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DOI：
10.1103/physrevb.108.l180302
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发表时间：
2023-05
影响因子：
3.7
通讯作者：
Ilyoun Na;Jack Kemp;Sin'ead M. Griffin;Robert-Jan Slager;Yang Peng
中科院分区：
文献类型：
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作者：
Ilyoun Na;Jack Kemp;Sin'ead M. Griffin;Robert-Jan Slager;Yang Peng
我们在存在动态时空对称性 $G$ 的情况下，在静态 Floquet 哈密顿量 $H_F$ 下使用酉环和频闪演化来考虑 Floquet 系统中的非平凡拓扑相。虽然后者一直是非平衡分类的主题，将具有额外晶体对称性的十倍方式和系统扩展到周期性驱动系统，但我们探索了 $H_F$ 中因动态时空对称性 $M$ 和 $G$ 的反对称性 $A$ 共存而出现的反常拓扑零模式，并使用频域公式对它们进行分类。此外，我们使用频率晶格提供了对所得 Floquet 拓扑相的解释，该频率晶格具有由晶格顶点上的颜色自由度表示的装饰。这些颜色对应于$G$沿频率格的群扩展$\tilde{G}$的系数$N$，由$N=Z\rtimes H^1[A,M]$给出。准能谱中不同能隙处出现的不同拓扑分类由对群扩展进行分类的上同调群 $H^{2}[G,N]$ 的挠积来描述。
We consider nontrivial topological phases in Floquet systems using unitary loops and stroboscopic evolutions under a static Floquet Hamiltonian $H_F$ in the presence of dynamical space-time symmetries $G$. While the latter has been subject of out-of-equilibrium classifications that extend the ten-fold way and systems with additional crystalline symmetries to periodically driven systems, we explore the anomalous topological zero modes that arise in $H_F$ from the coexistence of a dynamical space-time symmetry $M$ and antisymmetry $A$ of $G$, and classify them using a frequency-domain formulation. Moreover, we provide an interpretation of the resulting Floquet topological phases using a frequency lattice with a decoration represented by color degrees of freedom on the lattice vertices. These colors correspond to the coefficient $N$ of the group extension $\tilde{G}$ of $G$ along the frequency lattice, given by $N=Z\rtimes H^1[A,M]$. The distinct topological classifications that arise at different energy gaps in its quasi-energy spectrum are described by the torsion product of the cohomology group $H^{2}[G,N]$ classifying the group extension.