Half隙的晶格外推的再检验
Reexamination of Finite-Lattice Extrapolation of Haldane Gaps
摘要：
本文提出了两种估算无限尺寸极限外推时的系统误差的方法，用于测量自旋为S=5的一维海森堡反铁磁体的Half带隙.基于Lanczos算法的数值对角化得到的有限尺寸间隙的大小，以前没有被报道。并对边界条件的变化进行了分析。我们成功地证明了我们的外推方法工作良好。S=1时的Halcohol间隙估计为$0.4104789 \pm 0.0000013$。我们成功地得到了S=5时的带隙，从而证实了$S\to\infty$中Half带隙的渐近公式.
英文摘要：
We propose two methods of estimating a systematic error in extrapolation to the infinite-size limit in the study of measuring the Haldane gaps of the one-dimensional Heisenberg antiferromagnet with the integer spin up to S=5. The finite-size gaps obtained by numerical diagonalizations based on Lanczos algorithm are presented for sizes that have not previously been reported. The changes of boundary conditions are also examined. We successfully demonstrate that our methods of extrapolation work well. The Haldane gap for S=1 is stimated to be $0.4104789 \pm 0.0000013$. We successfully obtain the gaps up to S=5, which make us confirm the asymptotic formula of the Haldane gap in $S\to\infty$.
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