  We show that scalar chiral order can be induced by four-spin exchanges in the
two-leg spin ladder, using the spin-chirality duality transformation and
matrix-product ansatz. Scalar-chiral-ordered states are found to be exact
ground states in a family of spin ladder models. In this scalar chiral phase,
there is a finite energy gap above the doubly degenerate ground states and a
$Z_2 \times Z_2 \times Z_2$ symmetry is fully broken. It is also shown that the
SU(4)-symmetric model, which is self-dual under the duality transformation, is
on a multicritical point surrounded by the staggered dimer phase, the staggered
scalar chiral phase, and the gapless phase.

Strongly Correlated Electrons;Statistical Mechanics