  We study a period-4 antiferromagnetic mixed quantum spin chain consisting of
three kinds of spins. When the ground state is singlet, the spin magnitudes in
a unit cell are arrayed as (s-t, s, s+t, s) with integer or half-odd integer s
and t (0 <= t < s). The spin Hamiltonian is mapped onto a nonlinear sigma model
(NLSM) in a previously developed method. The resultant NLSM includes only two
independent parameters originating from four exchange constants for fixed s and
t. The topological angle in the NLSM determines the gapless phase boundaries
between disordered phases in the parameter space. The phase diagrams for
various s and t shows rich structures. We systematically explain the phases in
the singlet-cluster-solid picture.
