Phase diagram and excitation spectra of the anisotropic Kitaev-Heisenberg model
Phys. Rev. B 113, 134421 – Published 13 April, 2026
DOI: https://doi.org/10.1103/8764-n3rj
Abstract
The phase diagram and spin excitation spectra of the Kitaev-Heisenberg model with bond anisotropy are investigated using the exact diagonalization algorithm and spin cluster perturbation theory. By adjusting the model parameters and anisotropy intensity, we comprehensively map the complete phase diagram and uncover the excitation spectral characteristics of each phase. Besides the Kitaev spin liquid phases, whose excitation spectra appear entirely as a continuum, the antiferromagnetic Néel and zigzag phases also display strong high-energy continua and significant renormalization of the magnon dispersions. In contrast, the magnon dispersions of the ferromagnetic and stripy phases align closely with the predictions of linear spin-wave theory. Bond anisotropy induces directional selectivity of the magnetic moments in the four magnetically ordered phases, depending on the interaction parameters. Furthermore, bond anisotropy lifts the gaplessness of the pseudo-Goldstone mode for magnetization along the axis, while maintaining the gapless nature for magnetization perpendicular to the axis. Our results demonstrate that quantum fluctuations do not destroy the gapless property, which may be inherited from the gapless phase in the one-dimensional limit, described by a conformal field theory with central charge .
