A Monte Carlo Method for Fermion Systems Coupled with Classical Degrees of Freedom
A Monte Carlo Method for Fermion Systems Coupled with Classical Degrees of Freedom
复制标题
与经典自由度耦合的费米子系统蒙特卡罗方法
DOI：
10.1143/jpsj.68.3853
复制
发表时间：
1999
影响因子：
1.7
通讯作者：
N. Furukawa
中科院分区：
文献类型：
--
作者：
Y. Motome;N. Furukawa
提出了一种新的费米子系统与经典自由度相互作用的蒙特卡罗方法。为了获得具有固定配置的经典变量的每个蒙特卡罗样本的权值，采用切比雪夫多项式对状态密度进行矩展开，而不是直接对角化费米子哈密顿量。这将cpu时间减少到O (N dim 2 log N dim)，而传统技术中的对角化时间为O (N dim 3)；N dim是哈密顿矩阵的维数。该方法的另一个优点是可以实现高效率的并行计算。这大大节省了蒙特卡罗计算的总cpu时间，因为蒙特卡罗权重的计算是瓶颈部分。并以双交换模型为例进行了应用。基准测试结果表明，即使在现实的cpu时间尺度内的三个维度上，也可以使用系统大小缩放进行系统调查。
A new Monte Carlo method is proposed for fermion systems interacting with classical degrees of freedom. To obtain a weight for each Monte Carlo sample with a fixed configuration of classical variables, the moment expansion of the density of states by Chebyshev polynomials is applied instead of the direct diagonalization of the fermion Hamiltonian. This reduces a cpu time to scale as O ( N dim 2 log N dim ) compared to O ( N dim 3 ) for the diagonalization in the conventional technique; N dim is the dimension of the Hamiltonian. Another advantage of this method is that parallel computation with high efficiency is possible. These significantly save total cpu times of Monte Carlo calculations because the calculation of a Monte Carlo weight is the bottleneck part. The method is applied to the double-exchange model as an example. The benchmark results show that it is possible to make a systematic investigation using a system-size scaling even in three dimensions within a realistic cpu timescale.