Spin-1/2 XX chain with three-site interactions: Spin-Peierls instability

We discuss the effect of multisite interactions on the spin-Peierls instability for a spin-1/2 XX chain with three-site interactions of (XZX + Y ZY)-type. By a Jordan-Wigner transformation we arrive at a model of spinless fermions on a chain with nearest-neighbor and next-nearest-neighbor hoppings. We compute the ground-state energy of the model for static lattice distortion patterns corresponding to dimerization and trimerization in order to identify the ground-state configuration of the lattice. The additional three-site interactions cause a number of new phases to appear in the ground-state phase diagram, including trimerized phases.