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The mixed diamond chain is a frustrated Heisenberg chain composed ofsuccessive diamond-shaped units with two kinds of spins of magnitudes S and S/2(S: integer). Ratio $lambda$ of two exchange parameters controls the strengthof frustration. With varying $lambda$, the Haldane state and several spincluster states appear as the ground state. A spin cluster state is a tensorproduct of exact local eigenstates of cluster spins. We prove that a spincluster state is the ground state in a finite interval of $lambda$. For S=1, wenumerically determine the total phase diagram consisting of five phases.

Exact spin-cluster ground states in a mixed diamond chain