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Utilizing the Fermi gas microscope, recently the MIT group has measured thespin transport of the Fermi Hubbard model starting from a spin-density-wavestate, and the Princeton group has measured the charge transport of the FermiHubbard model starting from a charge-density-wave state. Motivated by these twoexperiments, we prove a theorem that shows under certain conditions, the spinand charge transports can be equivalent to each other. The proof makes use ofthe particle-hole transformation of the Fermi Hubbard model and a recentlydiscovered symmetry protected dynamical symmetry. Our results can be directlyverified in future cold atom experiment with the Fermi gas microscope.

On the Equivalence between Spin and Charge Dynamics of the Fermi Hubbard Model