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Floquet engineering is a powerful tool that drives materials with periodic light. Traditionally, the light is monochromatic, with amplitude, frequency, and polarization varied. We introduce Floquet engineering via unpolarized light built from quasi-monochromatic light, and show how it can modify strongly correlated systems, while preserving the original symmetries. Different types of unpolarized light can realize different strongly correlated phases As an example, we treat insulating magnetic materials on a triangular lattice and show how unpolarized light can induce a Dirac spin liquid.

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