We derive a complete classification of Floquet phases of interacting bosons and fermions with U(1) symmetry in two spatial dimensions. According to our classification, there is a one-to-one correspondence between these Floquet phases and rational functions π(z)=a(z)/b(z), where a(z) and b(z) are polynomials obeying certain conditions and z is a formal parameter. The physical meaning of π(z) involves the stroboscopic edge dynamics of the corresponding Floquet system: in the case of bosonic systems, π(z)=pq⋅˜π(z), where pq is a rational number that characterizes the flow of quantum information at the edge during each driving period and ˜π(z) is a rational function which characterizes the flow of U(1) charge at the edge. A similar decomposition exists in the fermionic case. We also show that ˜π(z) is directly related to the time-averaged U(1) current that flows in a particular geometry. This U(1) current is a generalization of the quantized current and quantized magnetization density found in previous studies of noninteracting fermionic Floquet phases.
ASJC Scopus subject areas
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics