Petersburg Nuclear Physics Institute, Gatchina, St Petersburg 188300, Russia.
J Phys Condens Matter. 2010 Jun 2;22(21):216003. doi: 10.1088/0953-8984/22/21/216003. Epub 2010 Apr 30.
The spectrum of short-wavelength magnons in a two-dimensional quantum Heisenberg antiferromagnet on a square lattice is calculated to the third order in a 1/S expansion. It is shown that a 1/S series for S = 1/2 converges quickly in the whole Brillouin zone except in the neighborhood of the point k = (π, 0), at which absolute values of the third-and the second-order 1/S-corrections are approximately equal to each other. It is shown that the third-order corrections make deeper the roton-like local minimum at k = (π, 0), improving the agreement with recent experiments and numerical results in the neighborhood of this point. It is suggested that the 1/S series converges slowly near k = (π, 0) also for S = 1 although the spectrum renormalization would be small in this case due to the very small values of high-order 1/S corrections.
在一个二维量子海森堡反铁磁体中，我们计算了在一个 1/S 展开中到第三阶的短波长磁振子的谱。结果表明，在整个布里渊区中，除了在点 k = (π, 0)附近之外，S = 1/2 的 1/S 级数收敛得非常快，在该点处，第三阶和二阶 1/S 修正的绝对值几乎相等。结果表明，三阶修正使得在 k = (π, 0)处的类转子局部最小值更深，从而提高了与该点附近最近的实验和数值结果的一致性。结果还表明，尽管在这种情况下，由于高阶 1/S 修正的非常小的值，谱重整化将很小，但对于 S = 1，在 k = (π, 0)附近，1/S 级数的收敛速度也很慢。
