Robust unidirectional phantom helix states in the XXZ Heisenberg model with Dzyaloshinskii-Moriya interaction

Phantom helix states are a special set of degenerate eigenstates the XXZ Heisenberg model which lie in energy levels around zero and bidirectionally equal. In this work, we study state with Dzyaloshinskii-Moriya interaction (DMI). We show exactly that only one direction remain unchanged presence resonant DMI. Based on Holstein-Primakoff transformation, quantum spin is mapped to boson model, allows us understand underlying mechanism. Furthermore, it also indicates such phantom can be separated from spectrum by strong DMI enhance robustness states. demonstrate dynamic formation processes unidirectional numerical simulations. The results indicate DMI, as expected, acts filter high efficiency.