  We develop a partial charge-spin separation fermion-spin theory implemented
the gauge invariant dressed holon and spinon. In this novel approach, the
physical electron is decoupled as the gauge invariant dressed holon and spinon,
with the dressed holon behaviors like a spinful fermion, and represents the
charge degree of freedom together with the phase part of the spin degree of
freedom, while the dressed spinon is a hard-core boson, and represents the
amplitude part of the spin degree of freedom, then the electron single
occupancy local constraint is satisfied. Within this approach, the charge
transport and spin response of the underdoped cuprates is studied. It is shown
that the charge transport is mainly governed by the scattering from the dressed
holons due to the dressed spinon fluctuation, while the scattering from the
dressed spinons due to the dressed holon fluctuation dominates the spin
response.
