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