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We propose a simple variational wave function that captures the correctground state energy of the spin-1 Heisenberg chain model to within 0.04\%. Thewave function is written in the matrix product state (MPS) form with the bonddimension $D=8$, and characterized by three fugacity parameters. The proposedMPS generalizes the Affleck-Kennedy-Lieb-Tasaki (AKLT) state by dressing itwith dimers, trimers, and general $q$-dimers. The fugacity parameters controlthe number and the average size of the $q$-mers. Furthermore, the $D=8$variational MPS state captures the ground states of the entire family ofbilinear-biquadratic Hamiltonian belonging to the Haldane phase to highaccuracy. The 2-4-2 degeneracy structure in the entanglement spectrum of ourMPS state is found to match well with the results of density matrixrenormalization group (DMRG) calculation, which is computationally muchheavier. Spin-spin correlation functions also find excellent fit with thoseobtained by DMRG.

Construction of Variational Matrix Product States for the Heisenberg Spin-1 Chain