Steady helix states in a resonant XXZ Heisenberg model with Dzyaloshinskii-Moriya interaction

Abstract

We systematically investigate possible helix states in the XXZ Heisenberg model with the Dzyaloshinskii-Moriya (DM) interaction. Exact solutions show that a set of precession helix states can be constructed by deliberate superposition of degenerate eigenstates of the Hamiltonian under the resonant condition. When a non-Hermitian balance boundary term is imposed as a quenching action, the quench dynamics shows that a steady helix state emerges from some easily prepared initial states, including saturated and maximally mixed ferromagnetic states, according to the analysis of the perturbation method. The corresponding dynamics for near resonant cases is also investigated numerically, indicating the robustness of the scheme. Our findings highlight the cooperation of non-Hermiticity and the DM interaction in a quantum spin system, suggesting a way for preparing a steady helix state in a non-Hermitian quantum spin system.