Effects of bond alternation and the Dzyaloshinskii-Moriya interaction on the ground-state phase diagram of the Ising model

The bond-alternative ferromagnetic Ising model with the Dzyaloshinskii-Moriya (DM) interaction is investigated using an infinite time-evolving block decimation (iTEBD) algorithm, and two interesting phase diagrams are proposed. Without bond alternation, there are only two well-known phases (a ferromagnetic phase and an x-y spiral (chiral Luttinger liquid) phase). Once the bond alternation is taken into account, two additional interesting phases (a z-chiral and a z-stripe phases) are induced. Nonzero chiral order is observed in all phases except the ferromagnetic phase. Two kinds of chiral phase, with or without string order, are identified. With the y-axis DM interaction, the phase diagram becomes relatively simple, and consists of only two different phases (a ferromagnetic phase and a y-chiral phase). First-order metamagnetic phase transitions from the ferromagnetic phase into the other phases are observed in both cases.