Kitaev Chain with Next-Nearest-Neighbor Spin Interactions

We use the density-matrix renormalization-group (DMRG) method to study a spin-1 Kitaev chain with added next-nearest-neighbor interactions between two spins. The Kitaev chain has broken rotational symmetry of the spins, and the additional next-nearest-neighbor spin interactions introduces further breaking of translational symmetry in the chain. We assume that the coupling constants for the next-nearest-neighbor spin interactions, K_x and K_y, can be adjusted for S^x and S^y components independently. As the different strength of next-nearest-neighbor spin interactions are tuned with respect to the strength of the Kitaev interaction, several phases emerge. A phase transition occurs in the region of comparable coupling constants K_x = K_y and in the region with a weak K_x and a finite K_y. We expect a deconfined quantum critical point (DQCP) to exist in this system under certain strength of these coupling constants. There may be a DQCP due to the breaking of two different symmetries in this system.