  We investigate the ground state properties of an S=1/2 distorted diamond
chain described by the Hamiltonian ${\cal
H}=J_1\sum_\ell\bigl\{\bigl(\vecS_{3\ell-1}\cdot\vecS_{3\ell}
+\vecS_{3\ell}\cdot\vecS_{3\ell+1}\bigr)+J_2\vecS_{3\ell-2}\cdot\vecS_{3\ell-1}
+J_3\bigl(\vecS_{3\ell-2}\cdot\vecS_{3\ell}+\vecS_{3\ell}\cdot\vecS_{3\
ell+2}\bigr)-H S_{\ell}^z\bigr\}$ ($J_1,~J_2,~J_3\geq0$), which models well a
trimerized S=1/2 spin chain system
Cu$_3$Cl$_6$(H$_2$O)$_2$$\cdot$2H$_8$C$_4$SO$_2$. Using an exact
diagonalization method by means of the Lancz\"os technique, we determine the
ground state phase diagram in the H=0 case, composed of the dimerized, spin
fluid, and ferrimagnetic phases. Performing a degenerate perturbation
calculation, we analyze the phase boundary line between the latter two phases
in the $J_2,~J_3\llJ_1$ limit, the result of which is in good agreement with
the numerical result. We calculate, by the use of the density matrix
renormalization group method, the ground state magnetization curve for the case
(a) where $J_1=1.0$, $J_2=0.8$, and $J_3=0.5$, and the case (b) where
$J_1=1.0$, $J_2=0.8$, and $J_3=0.3$. We find that in the case (b) the
2/3-plateau appears in addition to the 1/3-plateau which also appears in the
case (a). The translational symmetry of the Hamiltonian $\cal H$ is
spontaneously broken in the 2/3-plateau state as well as in the dimerized
state.
