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Spin Waves in Antiferromagnetic Spin Chains with Long Range Interactions

Eddy Yusuf·Anuvrat Joshi·Kun Yang
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Abstract

We study antiferromagnetic spin chains with unfrustrated long-range interactions that decays as a power law with exponent $β$, using the spin wave approximation. We find for sufficiently large spin $S$, the Neel order is stable at T=0 for $β< 3$, and survive up to a finite Neel temperature for $β< 2$, validating the spin-wave approach in these regimes. We estimate the critical values of $S$ and $T$ for the Neel order to be stable. The spin wave spectra are found to be gapless but have non-linear momentum dependence at long wave length, which is responsible for the suppression of quantum and thermal fluctuations and stabilizing the Neel state. We also show that for $β\le 1$ and for a large but finite-size system size $L$, the excitation gap of the system approaches zero slower than $L^{-1}$, a behavior that is in contrast to the Lieb-Schulz-Mattis theorem.

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Eddy Yusuf, Anuvrat Joshi, Kun Yang. 2004-05-10. Spin Waves in Antiferromagnetic Spin Chains with Long Range Interactions. https://doi.org/10.1103/physrevb.69.144412

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