Ground-state phase diagram of the spin-1/2-1/2-1-1 chain

We investigate the ground-state phase diagram of the quantum mixed spin cha in in which two S = 1/2 and two S=1 spins are arranged alternatively and is otropic exchange interactions between nearest-neighboring pairs of spins ar e assumed. Guided by our previous results [J. Phys. Sec. Jpn. 67 (1998) 100 0] for a few limiting cases of the exchange interactions, we carry out a de nsity-matrix renormalization-group calculation to determine the ground-stat e phase diagram in detail. From the gapless points of the singlet-triplet e nergy gap, five boundary lines are determined, which divide the phase diagr am into six regions. In three regions the ground states with the Haldane-ph ase character appear, while in the remaining three regions those with the d imer character appear. We also present a characterization of the phases con cerning how the ground state in each phase is represented in the framework of the valence-bond-solid (VBS) picture. Making use of the matrix-product w ave function, we classify the VBS pictures and interpret the ground-state p hase diagram in terms of symmetries schematically related to the VBS pictur es. We investigate the ground-state nearest-neighboring two-spin correlatio n functions and a kind of string order parameters, by which we confirm the validity of the characterization.