A new family of models with exact ground states connecting smoothly the S=1/2 dimer and S=1 Haldane phases of 1D 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 which have a matrix product wavefunction as 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. This proves that these model systems are in the same phase. We also present a new set of models of frustrated S=1/2 spin chains (including only bilinear NN and NNN interactions) whose ground states can be found exactly.