Spin waves in antiferromagnetic spin chains with long-range interactions

We study antiferromagnetic spin chains with unfrustrated long-range interactions that decay as power laws with exponent $\beta ,$ using the spin-wave approximation. We find for sufficiently large spin S that the Neel order is stable at $T=0\mathrm{}$ for $\beta <3,$ and survives up to a finite Neel temperature for $\beta <2,$ 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 nonlinear momentum dependence at long wavelength, which is responsible for the suppression of quantum and thermal fluctuations and stabilizing the Neel state. We also show that for $\beta <~1$ 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-Schultz-Mattis theorem.