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