Kernel Polynomial Approximations for Densities of States and Spectral Functions
Kernel Polynomial Approximations for Densities of States and Spectral Functions
复制标题
态密度和谱函数的核多项式近似
DOI：
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发表时间：
1996
期刊：
影响因子：
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通讯作者：
J. Kress
中科院分区：
文献类型：
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作者：
R. Silver;H. Roeder;A. Voter;J. Kress
切比雪夫多项式近似是一种有效且数值稳定的方法来计算在计算凝聚态物理中非常重要的超大哈密顿量的性质。本文推导了一种最优核多项式，它加强了状态密度和谱估计的正性，达到了最佳的能量分辨率，并保持了归一化。这种核多项式方法(KPM)被用来计算电子结构和动态磁化率。对于Si的紧束缚哈密顿量，我们展示了如何通过仔细注意近似的顺序来实现结合能和空位形成能的高精度和快速收敛。对于无序XXZ磁体，我们证明了KPM提供了一种比Lanczos递推方法更简单和更可靠的计算谱函数的方法。还给出了费米投影算子的多项式逼近。
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 states 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.