Current response in extended systems as a geometric phase: Application to variational wavefunctions
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.