Spin helix states with spatially modulated spin textures are exact eigenstates of the one-dimensional anisotropic spin-$\frac{1}{2}$ Heisenberg model under specific parameter conditions. In this work, we extend this framework by constructing exact eigenstates of the fully anisotropic XYZ Heisenberg model, with spin helix structures modulated by elliptic functions, across all spatial dimensions and spin quantum numbers. The XXZ and XY cases are also analyzed to clarify the conditions for the emergence of spin helix eigenstates and their key properties. Within the subspace spanned by these elliptic spin helix states, a family of analytically tractable states can be identified. Our results broaden the class of exactly solvable eigenstates in nonintegrable systems and deepen the understanding of spin modulation states in many-body systems.

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• Mathematical physics
• Quantum scars
• Strongly correlated systems
• Exact solutions for many-body systems
• Heisenberg model
• Integrable systems
• Lattice models in condensed matter
• XYZ model