Quantum phase transitions in the spin-1/2 XXZ model with staggered γ interaction

The one-dimensional spin-1/2 XXZ model with the limited case of the staggered Gamma interaction which includes the staggered DM and KSEA interactions is investigated by utilizing the infinite-time evolving block decimation method in the infinite matrix product state representation. It is shown that the staggered DM interaction does not lead to any new phase but expands the XY phase. Contrasted to the DM interaction, the region of the ferromagnetic phase expands into the nematic-ferromagnetic and dimer-Haldane phases with the deconfined quantum phase transition happening in the case of KSEA interaction. We observe a pronounced effect in the entanglement entropy and Schmidt gap, the odd-bond and even-bond von Neumann entropies exhibit different values, and the value of the Schmidt gap on the even bond becomes zero in the dimer-Haldane phase. This implies that quantum entanglement and the Schmidt gap can distinguish the two degenerate ground states caused by the existence of dimerized interaction. The zero value of the Schmidt gap works as a sign of the topological phase, which is also evidenced by the string correlation. From the perspective of magnetism, the existence of chiral order and nematic order suggests the helical magnetic structure induced by Gamma interaction. By comparing the DM and KSEA interactions, it is found that DM interaction does not change ferromagnetism, whereas the KSEA interaction inhibits ferromagnetism and destroys the product state in the ferromagnetic phase. Furthermore, the behaviors of the spin structure factor for the transversal spin correlation can distinguish different phases. From an appropriate fitting exponent of the spin correlation oscillating decay, commensurate or incommensurate phases can be identified.