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Special Quantum Matter Seminar

Friday, October 20, 2023
3:00pm to 4:00pm
Add to Cal
East Bridge 114
Floquet Gap-dependent topological classifications from color-decorated frequency lattices with space-time symmetries
Iryan Na, Department of Physics, UC Berkely,

We find a new class of Floquet topological phases exhibiting gap-dependent topological classifications in quantum systems with a dynamical space-time symmetry and an antisymmetry. This is in contrast to all existing Floquet topological phases protected by static symmetries, where the topological classifications across all quasi-energy gaps are characterized by the same Abelian group. We illustrate this gap-dependent classification using the frequency-domain formulation of the time-dependent Hamiltonian. 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 of the symmetry group $G$ 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.