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

• URL: http://arxiv.org/abs/2010.02253v1
• Date: Mon, 5 Oct 2020 18:07:57 GMT
• Title: Classification of interacting Floquet phases with $U(1)$ symmetry in two dimensions
• Authors: Carolyn Zhang and Michael Levin
• Abstract summary: We derive a complete classification of Floquet phases of interacting bosons and fermions with $U(1)$ symmetry in two dimensions. According to our classification, there is a one-to-one between these Floquet phases and rational functions $pi(z)$. We also show that $tildepi(z)$ is directly related to the time-averaged $U(1)$ current that flows in a particular geometry.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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, $\pi(z) = \frac{p}{q} \cdot \tilde{\pi}(z)$ where $\frac{p}{q}$ is a rational number which characterizes the flow of quantum information at the edge during each driving period, and $\tilde{\pi}(z)$ 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 $\tilde{\pi}(z)$ 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 non-interacting fermionic Floquet phases.

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