Non-linear spin wave theory in the strong easy-axis limit of the triangular XXZ model

Achille Mauri; Siebe Roose; Frédéric Mila

doi:10.1103/57w8-31vp

paper

Non-linear spin wave theory in the strong easy-axis limit of the triangular XXZ model

arXiv:2511.08179 · doi:10.1103/57w8-31vp

Abstract

Motivated by recent experimental studies, we investigate the spectrum of the nearest-neighbour triangular XXZ model within the $1/ S$ expansion, in the limit in which the exchange couplings present a strong easy-axis anisotropy $J_{x y} / J_{z z} ≪ 1$ . We show that in the limit in which $1/ S \to 0$ and $J_{x y} \to 0$ at fixed $V = J_{z z} / (S J_{x y})$ , the triangular spin model can be reduced to an effective boson model with quartic interactions on the honeycomb lattice. This effective model interpolates between a spin-wave ( $V \to 0$ ) and a strong-coupling limit ( $V \to \infty$ ) and encodes in a simple framework the regimes discussed by Kleine~\emph{et al.}~[Z. Phys. B Condens. Matter~{\bf 86}, 405 (1992);~{\bf 87}, 103 (1992)]. For zero field, the classical ground state of the model presents an accidental degeneracy, which can be traced to a simple symmetry of the classical energy. The model thus offers a transparent realization of a theory with quantum order-by-disorder and a pseudo-Goldstone mode. We analyze the spectrum at zero magnetic field by calculating the self-energy at one-loop order. In the calculation, we introduce a self-consistent renormalization of the energy scale and of the pseudo-Goldstone energy gap; the latter renormalization is essential to remove infrared divergences in the on-shell corrections to the energy dispersion. Finally, we discuss qualitatively the structure of the one-loop corrections in comparison with the spectrum observed experimentally in K $_{2}$ Co(SeO $_{3}$ ) $_{2}$ .

28 pages, 13 figures

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