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Abstract The Gauge field theory is a fundamental concept in modern physics, attracting many theoretical and experimental efforts towards its simulation. In this paper, we propose that a simple model, in which fermions coupled to a dynamical lattice gauge field, can be engineered via the Floquet approach. The model possesses both an independent Maxwell term and the local Z 2 gauge symmetry. Our proposal relies on a speciesdependent optical lattice, and can be achieved in one, two or three dimensions. By a unitary transformation, this model can be mapped into a non-interacting composite fermion system with fluctuating background charge. With the help of this composite fermion picture, two characteristic observations are predicted. One is the radio-frequency spectroscopy, which exhibits no dispersion in all parameter regimes. Second is the dynamical localization, which depends on the structure of the initial states.
Sun et al. (Fri,) studied this question.