  Many strongly correlated materials are characterized by deeply intertwined
charge and spin order. Besides their high superconducting transition
temperatures, one of the central features of these complex patterns in cuprates
is a phase shift which occurs across lines of decreased hole density. That is,
when doped away from their AF phase, the additional charge is not distributed
uniformly, but rather in `stripes'. The sublattices preferentially occupied by
up and down spin are reversed across these stripes, a phenomonenon referred to
as a `$\pi$-phase shift'. Many of the spin-charge patterns, including the
$\pi$-phase shift, are reproduced by Density Matrix Renormalization Group and
Quantum Monte Carlo calculations of simplified tight binding (repulsive
Hubbard) models. In this paper we demonstrate that this sublattice reversal is
generic by considering the corresponding phenomenon in the attractive Hubbard
Hamiltonian, where a charge density wave phase forms at half-filling. We
introduce charge stripes via an appropriate local chemical potential;
measurements of charge correlation across the resulting lines of lowered
density reveal a clear $\pi$ phase.
