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

Abstract

We systematically investigate possible helix states in XXZ Heisenberg model with 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 saturate and maximally mixed ferromagnetic states, according to the analysis of 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 quantum spin system, suggesting a way for preparing steady helix state in non-Hermitian quantum spin system.

9 pages, 4 figures

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Cited by in corpus (7)

• Universality in relaxation of spin helices under the $XXZ$- spin chain dynamics
• All product eigenstates in Heisenberg models from a graphical construction
• Stable dynamic helix state in the nonintegrable XXZ Heisenberg model
• Robust unidirectional phantom helix states in the XXZ Heisenberg model with Dzyaloshinskii-Moriya interaction
• Exact NESS of XXZ circuits boundary driven with arbitrary resets or fields
• Real space thermalization of locally driven quantum magnets
• Stabilization of Granovskii-Zhedanov scars of the XYZ quantum spin chain via non-Hermitian spin relaxation