We present a new method of constructing the matrix product (MP) states and apply it to the ground state of the Heisenberg spin chain with alternating spins 1 and 1 2 and antiferromagnetic exchange interactions between nearest neighbors (the simplest example of a quantum ferrimagnet). The elementary matrix state is constructed in a way which ensures given transformational properties under rotations, which allows one to fix the total spin and its z-projection of the entire MP wavefunction. We compare the variational MP results with the numerical results obtained through a Quantum Monte Carlo method; the agreement is found to be within 0.4% for the ground state energy and 5% for the correlation functions.
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