Calculating the linear response functions of noninteracting electrons with a time-dependent Schrödinger equation
Calculating the linear response functions of noninteracting electrons with a time-dependent Schrödinger equation
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DOI：
10.1103/physreve.56.1222
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发表时间：
1997-03
影响因子：
2.4
通讯作者：
T. Iitaka;S. Nomura;H. Hirayama;Xinwei Zhao;Y. Aoyagi;T. Sugano
中科院分区：
文献类型：
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作者：
T. Iitaka;S. Nomura;H. Hirayama;Xinwei Zhao;Y. Aoyagi;T. Sugano
提出了一种计算任意势下非相互作用电子线性响应函数的O(N)算法。该算法基于空间离散化的时变薛定谔方程的数值解，适用于并行计算和矢量计算。由于它避免了矩阵对角化的O（N^3）计算量，因此只需要O(N)计算量，其中N是状态向量的维数。这种O(N)算法对于由数千个原子组成的系统是非常有效的，因为否则我们必须计算大量的特征态，即，占满了费米能量的单电子态和具有更高能量的未占态。该方法与最近由Wang （L.W. Wang, Phys.）提出的Chebyshev多项式方法相比具有优势。中国生物医学工程学报，2004 (1)王、phy。Rev. Lett. 73, 1039(1994))是我们的方法可以计算线性响应函数，而无需在外部存储器上存储任何巨大的状态器。因此，它可以处理更大的系统。
An O(N) algorithm is proposed for calculating linear response functions of non-interacting electrons in arbitray potential. This algorithm is based on numerical solution of the time-dependent Schroedinger equation discretized in space, and suitable to parallel- and vector- computation. Since it avoids O(N^3) computational effort of matrix diagonalization, it requires only O(N) computational effort where N is the dimension of the statevector. This O(N) algorithm is very effective for systems consisting of thousands of atoms, since otherwise we have to calculate large number of eigenstates, i.e., the occupied one-electron states up to the Fermi energy and the unoccupied states with higher energy. The advantage of this method compared to the Chebyshev polynomial method recently developed by Wang (L.W. Wang, Phys. Rev. B49, 10154 (1994);L.W. Wang, Phys. Rev. Lett. 73, 1039 (1994)) is that our method can calculate linear response functions without any storage of huge statevectors on external storage. Therefore it can treat much larger systems.