arXiv:cond-mat/9303010v1 8 Mar 1993 Phase diagram of the S = 1 2 quantum spin chain with bond alternation M. Yamanaka, Y. Hatsugai * and M. Kohmoto Institute for Solid State Physics, University of Tokyo 7-22-1, Roppongi, Minato-ku, Tokyo 106 Japan We study the ground state properties of the bond alternating S =1/2 quantum spin chain whose Hamiltonian is H =  j (S x 2j S x 2j +1 + S y 2j S y 2j +1 + λS z 2j S z 2j +1 )+ β  j S 2j -1 · S 2j . (0.1) When β = 0, the ground state is a collection of local singlets with a finite excitation gap. In the limit of strong ferromagnetic coupling β → −∞, this is equivalent to the S =1 XXZ Hamiltonian. It has several ground state phases in the λ-β plane including the gapful Haldane phase. They are characterized by a full breakdown, partial breakdowns and a non-breakdown of the hidden discrete Z 2 × Z 2 symmetry. The ground state phase diagram is obtained by series expansions. PACS numbers: 75.10.Jm, 75.50.Gg, 75.30.Kz Typeset Using REVTEX 1