Models with exact ground states connecting smoothly the S=1/2 dimer and S=1 Haldane phases of one-dimensional spin chains

We investigate the isotropic two-leg S = 1/2 ladder with general bilinear and biquadratic exchange interactions between spins on neighboring rungs, and determine the Hamiltonians that have a matrix-product wave function as an exact ground state. We demonstrate that a smooth change of parameters leads one from the S = 1/2 dimer and Majumdar-Ghosh chains to the S=1 chain with biquadratic exchange, which proves that these model systems are in the same phase. The family of Hamiltonians also includes a set of models of isotropic S = 1/2 chains with only bilinear nearest-and next-nearest-neighbor interactions. The ground state for these models becomes unstable at a line of first-order phase transitions to the ferromagnetic state. [S0163-1829(97)50342-0].