Improved Multi-Variable Variational Monte Carlo Method Examined by High-Precision Calculations of One-Dimensional Hubbard Model
Improved Multi-Variable Variational Monte Carlo Method Examined by High-Precision Calculations of One-Dimensional Hubbard Model
复制标题
一维哈伯德模型高精度计算检验改进的多变量变分蒙特卡罗方法
DOI：
10.1088/1742-6596/454/1/012046
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
Masatoshi Imada
中科院分区：
文献类型：
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作者：
Ryui Kaneko;Satoshi Morita;Masatoshi Imada
我们以一维Hubbard模型的基态性质为例，重新审视变分蒙特卡罗（VMC）方法的准确性。我们从卡佩罗等人引入的Gutzwiller和远程Jastrow因子的变分波函数开始。Rev. B 72, 085121(2005)]并通过考虑几个量子数投影和广义的单体波函数进一步改进它。我们发现量子自旋投影和总动量投影大大提高了基态能量的精度，误差在0.5%以内，对于小系统和大系统都是如此。此外，在196个位置计算的四分之一填充时的动量分布函数n (k)允许我们从费米波矢量附近n (k)的幂律行为直接估计电荷相关的临界指数。估计的临界指数很好地再现了Tomonaga-Luttinger理论所预测的那些指数。
We revisit the accuracy of the variational Monte Carlo (VMC) method by taking an example of ground state properties for the one-dimensional Hubbard model. We start from the variational wave functions with the Gutzwiller and long-range Jastrow factor introduced by Capello et al.[Phys. Rev. B 72, 085121 (2005)] and further improve it by considering several quantum-number projections and a generalized one-body wave function. We find that the quantum spin projection and total momentum projection greatly improve the accuracy of the ground state energy within 0.5% error, for both small and large systems at half filling. Besides, the momentum distribution function n (k) at quarter filling calculated up to 196 sites allows us direct estimate of the critical exponents of the charge correlations from the power-law behavior of n (k) near the Fermi wave vector. Estimated critical exponents well reproduce those predicted by the Tomonaga-Luttinger theory.