  We present a variational matrix product state (vMPS) for the ground state of
the spin-1/2 Heisenberg model. The MPS effectively organizes the various dimer
configurations, in faithful reflection of the resonating valence bond (RVB)
picture of the spin liquid, with the energy only 0.024% higher than the exact
value given by Bethe ansatz. Building on the ground-state vMPS, the one-spin
wave function is constructed in a simple manner with the dispersion that
matches well with the exact spectrum. The vMPS scheme is applied to the family
of Hamiltonian extrapolating between the Heisenberg model and the
Majumdar-Ghosh model.
