  A new method of writing down the path integral for spin-1 Heisenberg
antiferromagnetic chain is introduced. In place of the conventional coherent
state basis that leads to the non-linear sigma-model, we use a new basis called
the fluctuating matrix product states (fMPS) which embodies inter-site
entanglement from the outset. It forms an overcomplete set spanning the entire
Hilbert space of the spin-1 chain. Saddle-point analysis performed for the
bilinear-biquadratic spin model predicts Affeck-Kennedy-Lieb-Tasaki (AKLT)
state as the ground state in the vicinity of the AKLT Hamiltonian. Quadratic
effective action derived by gradient expansion around the saddle point is free
from constraints that plagued the non-linear sigma model and exactly solvable.
The obtained excitation modes agree precisely with the single-mode
approximation result for the AKLT Hamiltonian. Excitation spectra for other
BLBQ Hamiltonians are obtained as well by diagonalizing the quadratic action.
