  Using the matrix product formalism, we define a multi-parameter family of
spin models on one dimensional chains, with nearest and next-nearest neighbor
anti-ferromagnetic interaction for which exact analytical expressions can be
found for its doubly degenerate ground states. The family of Hamiltonians which
we define, depend on 5 continuous parameters and the Majumdar-Ghosh model is a
particular point in this parameter space. Like the Majumdar-Ghosh model, the
doubly degenerate ground states of our models have a very simple structure,
they are the product of entangled states on adjacent sites. In each of these
states there is a non-zero staggered magnetization, which vanishes when we take
their translation-invariant combination as the new ground states. At the
Majumdar-Ghosh point, these entangled states become the spin-singlets
pertaining to this model. We will also calculate in closed form the two point
correlation functions, both for finite size of the chain and in the
thermodynamic limit.
