Topological Micromotion of Floquet Quantum Systems
- URL: http://arxiv.org/abs/2106.14628v2
- Date: Sat, 26 Feb 2022 01:52:05 GMT
- Title: Topological Micromotion of Floquet Quantum Systems
- Authors: Peng Xu, Wei Zheng, and Hui Zhai
- Abstract summary: We show that an accurate description of a Floquet system requires a set of Hamiltonian exhausting all values of the micro-motion parameter.
We show that a $d$-dimensional Floquet system can be described by a $d+1$-dimensional static Hamiltonian.
- Score: 5.76844077446399
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The Floquet Hamiltonian has often been used to describe a time-periodic
system. Nevertheless, because the Floquet Hamiltonian depends on a micro-motion
parameter, the Floquet Hamiltonian with a fixed micro-motion parameter cannot
faithfully represent a driven system, which manifests as the anomalous edge
states. Here we show that an accurate description of a Floquet system requires
a set of Hamiltonian exhausting all values of the micro-motion parameter, and
this micro-motion parameter can be viewed as an extra synthetic dimension of
the system. Therefore, we show that a $d$-dimensional Floquet system can be
described by a $d+1$-dimensional static Hamiltonian, and the advantage of this
representation is that the periodic boundary condition is automatically imposed
along the extra-dimension, which enables a straightforward definition of
topological invariants. The topological invariant in the $d+1$-dimensional
system can ensure a $d-1$-dimensional edge state of the $d$-dimensional Floquet
system. Here we show two examples where the topological invariant is a
three-dimensional Hopf invariant. We highlight that our scheme of classifying
Floquet topology on the micro-motion space is different from the previous
classification of Floquet topology on the time space.
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