  Using gauge transformations on electron bond operators, we derive exact
duality relations between various order parameters for correlated electron
systems. Applying these transformations, we find two duality relations in the
generalized two-leg Hubbard ladder at arbitrary filling. The relations show
that unconventional density-wave orders such as staggered flux or circulating
spin-current are dual to conventional density-wave orders and there are direct
mappings between dual phases. Several exact results on the phase diagram are
also concluded.
