Transition from Haldane phase to spin liquid and incommensurate correlation in spin-1/2 Heisenberg chains

The bulk properties and impurity effect in the one-dimensional S = 1/2 Heisenberg model with dimerization and next-nearest-neighbor exchange are studied by the density matrix renormalization group and exact diagonalization methods. This model widely covers the S = 1 Heisenberg model, two-leg ladders, bond-alternating chains and the S = 1/2 Heisenberg model. Almost the whole parameter space belongs to the Haldane phase. In the non-dimerizing limit a transition to a kind of spin liquid takes place, characterized by the delocalized spin polarization. This transition causes the distinct impurity effects between a spin-Peierls compound CuGeO₃ and the Haldane systems. Experimental aspects of a bond-alternating compound CuNb₂O₆ are also discussed. Furthermore, the incommensurate correlation arising in this model is extensively studied, and a phase diagram is constructed.