Non-linear spin wave theory in the strong easy-axis limit of the triangular XXZ model
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| Format: | Preprint |
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2025
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| _version_ | 1866914600899837952 |
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| author | Mauri, Achille Roose, Siebe Mila, Frédéric |
| author_facet | Mauri, Achille Roose, Siebe Mila, Frédéric |
| contents | 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 $J_{xy}/J_{zz} \ll 1$. We show that in the limit in which $1/S \to 0$ and $J_{xy} \to 0$ at fixed $V = J_{zz}/(S J_{xy})$, 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$_{3}$)$_{2}$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_08179 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-linear spin wave theory in the strong easy-axis limit of the triangular XXZ model Mauri, Achille Roose, Siebe Mila, Frédéric Strongly Correlated Electrons 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 $J_{xy}/J_{zz} \ll 1$. We show that in the limit in which $1/S \to 0$ and $J_{xy} \to 0$ at fixed $V = J_{zz}/(S J_{xy})$, 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$_{3}$)$_{2}$. |
| title | Non-linear spin wave theory in the strong easy-axis limit of the triangular XXZ model |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2511.08179 |