Effect of Dzyaloshinskii–Moriya interaction on phase diagrams of spin-1 Heisenberg–Ising alternating chains

Abstract The effect of the Dzyaloshinskii–Moriya interaction (DMI) on ground-state phase diagrams of spin-1 Heisenberg–Ising alternating chains is investigated by the infinite time-evolving block decimation method. Three rich phase diagrams for three cases with different DMIs are obtained and discussed systematically. The DMI on even bonds plays a key role in the ground-state phase diagram, especially the appearance of the Haldane phase. However, the DMI on odd bonds seems to have very weak effect on the phase diagram. Both the odd- and even-string orders become nonzero in the Haldane phase, and have their maximum values at θ = π . For the odd-dimer phase, the even-string correlator vanishes absolutely despite varying θ , but a double-peak structure of the odd-string correlator is observed. Odd-string correlator becomes maximum at θ = π / 2 and 3 π / 2 , but vanishes at θ = π . It indicates that the generalized string correlator can be used to distinguish the odd-dimer from the Haldane phase. Doubly degenerate entanglement spectrum is observed in the Haldane phase, which can be regarded as a clear signature of the existence of topological orders. Strong enough transverse nearest-neighbor correlations are found to be very important for the appearance of the Haldane and the odd-dimer phases.