Classification of interacting Floquet phases with U(1) symmetry in two dimensions

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 pi(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 pi(z) involves the stroboscopic edge dynamics of the corresponding Floquet system: in the case of bosonic systems, pi(z) = p/q. (pi) over tilde (z), where p/q is a rational number that characterizes the flow of quantum information at the edge during each driving period and (pi) over tilde (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 (pi) over tilde (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.

Automated summary

In this study, a complete classification of Floquet phases of interacting bosons and fermions with U(1) symmetry in two spatial dimensions was derived, revealing a one-to-one correspondence with rational functions. These rational functions have significant physical meanings related to the stroboscopic edge dynamics of the corresponding systems, such as characterizing the flow of quantum information and U(1) charge at the edge. Additionally, the rational function (pi) over tilde (z) was shown to be directly linked to the time-averaged U(1) current flowing in a specific geometry, serving as a generalization of previously discovered quantized current and magnetization density in noninteracting fermionic Floquet phases.