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

TL;DR

This paper explores how steady helix states can be generated and maintained in a non-Hermitian XXZ Heisenberg model with Dzyaloshinskii-Moriya interaction, revealing a method for state preparation in quantum spin systems.

Contribution

It introduces a novel approach to create and stabilize helix states using non-Hermitian boundary conditions and resonant interactions in a quantum spin model.

Findings

Exact solutions for precession helix states under resonance.

Steady helix states emerge from specific initial states after quenching.

Robustness of the scheme demonstrated through numerical analysis.

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.