Exact spin helix eigenstates in the anisotropic spin-$s$ Heisenberg model with arbitrary dimensions

TL;DR

This paper constructs exact spin helix eigenstates for the anisotropic XYZ Heisenberg model across arbitrary dimensions and spins, revealing persistent non-trivial eigenstates beyond integrability.

Contribution

It extends the known spin helix eigenstates from 1D spin-1/2 models to fully anisotropic XYZ models with arbitrary dimensions and spins, broadening analytical understanding.

Findings

Exact eigenstates exist in non-integrable regimes.

Spin helix states are characterized in XYZ models.

Conditions for eigenstate emergence are clarified.

Abstract

Spin helix states-characterized by their 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 spin helix eigenstates for the fully anisotropic XYZ Heisenberg model with arbitrary spatial dimensions and arbitrary spin quantum numbers. Our results demonstrate that some non-trivial exact eigenstates can persist beyond the integrable regime. The XXZ and XY cases are also analyzed to clarify the conditions for the emergence of spin helix eigenstates and their key properties. Our results broaden the class of analytically tractable exact eigenstates in non-integrable systems and deepen understanding of spin modulation states in many-body systems.