  The linear response theory for current is investigated in a variational
context. Expressions are derived for the Drude and superfluid weights for
general variational wavefunctions. The expression for the Drude weight
highlights the difficulty in its calculation since it depends on the exact
energy eigenvalues which are usually not available in practice. While the Drude
weight is not available in a simple form, the linear current response is shown
to be expressible in terms of a geometric phase, or alternatively in terms of
the expectation value of the total position shift operator. The contribution of
the geometric phase to the current response is then analyzed for some commonly
used projected variational wavefunctions (Baeriswyl, Gutzwiller, and combined).
It is demonstrated that this contribution is independent of the projectors
themselves and is determined by the wavefunctions onto which the projectors are
applied.
