Incommensurate Matrix Product State for Quantum Spin Systems

Understand

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 spin rotations decrease the variational energy with accompanying translational symmetry breaking and the rotational symmetry breaking in the spin space even if the Hamiltonian has the both symmetries.
• The optimized pitch of rotational operator reflects the commensurate/incommensurate properties of spin-spin correlation functions in the $S=1/2$ Heisenberg chain and the $S=1/2$ ferro-antiferro zigzag chain.