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首页> 外文期刊>Journal of Computational Physics >KERNEL POLYNOMIAL APPROXIMATIONS FOR DENSITIES OF STATES AND SPECTRAL FUNCTIONS
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KERNEL POLYNOMIAL APPROXIMATIONS FOR DENSITIES OF STATES AND SPECTRAL FUNCTIONS

机译：状态密度和谱函数的核多项式逼近

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摘要

Chebyshev polynomial approximations are an efficient and numerically stable way to calculate properties of the very large Hamiltonians important in computational condensed matter physics. The present paper derives an optimal kernel polynomial which enforces positivity of density of stales and spectral estimates, achieves the best energy resolution, and preserves normalization. This kernel polynomial method (KPM) is demonstrated for electronic structure and dynamic magnetic susceptibility calculations. For tight binding Hamiltonians of Si, we show how to achieve high precision and rapid convergence of the cohesive energy and vacancy formation energy by careful attention to the order of approximation. For disordered XXZ-magnets, we show that the KPM provides a simpler and more reliable procedure for calculating spectral functions than Lanczos recursion methods. Polynomial approximations to Fermi projection operators are also proposed. (C) 1996 Academic Press, Inc. [References: 26]
机译：切比雪夫多项式逼近是一种有效且数值稳定的方法，用于计算在计算凝聚态物理中很重要的非常大的哈密顿量的性质。本文推导了一个最优核多项式，该多项式可增强实测密度和频谱估计的正性，实现最佳能量分辨率，并保持归一化。该核多项式方法（KPM）用于电子结构和动态磁化率计算。对于Si的紧密结合哈密顿量，我们展示了如何通过密切关注近似顺序来实现内聚能和空位形成能的高精度和快速收敛。对于无序XXZ磁体，我们证明，与Lanczos递归方法相比，KPM为计算频谱函数提供了一种更简单，更可靠的过程。还提出了费米投影算子的多项式近似。 （C）1996 Academic Press，Inc. [参考：26]

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