Irregular parameter dependence of numerical results in tensor renormalization group analysis
Irregular parameter dependence of numerical results in tensor renormalization group analysis
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DOI：
10.1093/ptep/ptz056
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发表时间：
2018-12
影响因子：
3.5
通讯作者：
D. Kadoh;Y. Kuramashi;Ryoichi Ueno
中科院分区：
文献类型：
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作者：
D. Kadoh;Y. Kuramashi;Ryoichi Ueno
研究了由张量重整化群得到的数值结果的参数依赖性。随着方法参数的变化，我们经常观察到不规则的行为。使用二维Ising模型，我们明确地表明，截断奇异值分解中使用的锐截断会导致这种不希望的行为，当截断阶以下和截断阶以上的奇异值之间发生水平交叉时，随着参数的变化。我们还测试了一个平滑的截止，而不是尖锐的截止，作为截断方案，并讨论了它的效果。
We study the parameter dependence of numerical results obtained by the tensor renormalization group. We often observe irregular behavior as the parameters are varied with the method. Using the two-dimensional Ising model we explicitly show that the sharp cutoff used in the truncated singular value decomposition causes this unwanted behavior when the level crossing happens between singular values below and above the truncation order as the parameters are varied. We also test a smooth cutoff, instead of the sharp one, as a truncation scheme and discuss its effects.