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 introduce further breaking of the translational symmetry in the chain. We assume that the coupling constants for the next-nearest-neighbor spin interactions, K_xand K_y, can be adjusted for the S_x and S_y components independently. As the different strengths of next-nearest-neighbor spin interactions are tuned with respect to the strength of the Kitaev interaction, a VBS phase and AFM phase emerge. A phase transition occurs along the line where Kx=-Ky, which coincides with a line of increased entanglement entropy. We find a peak in the entanglement entropy along this line. We further investigate whether a deconfined quantum critical point (DQCP) and weak first-order quantum phase transition coexist in this transition under different strength of coupling.