We introduce a matrix product state (MPS) with an incommensurate periodicity by applying the spin-rotation operator of each site to a uniform MPS in the thermodynamic limit. The relation between the improvement of the variational method due to the spin-rotation operators and the spontaneous symmetry breaking of the MPS is studied. The optimized pitch of the rotational operator reflects the commensurate/incommensurate properties of spin-spin correlation functions in the $S=1/2$ Heisenberg chain and the $S=1/2$ ferromagnetic-antiferromagnetic zigzag chain.

• Received 9 May 2012

DOI:https://doi.org/10.1103/PhysRevB.86.064438