Kpm method.

Background

Refer to

https://kwant-project.org/doc/dev/tutorial/kpm

A. Weisse, G. Wellein, A. Alvermann, and H. Fehske, “The Kernel Polynomial Method,” Rev. Mod. Phys. 78(1), 275–306 (2006).

params

Two parameters control the effect of the algorithm.
The number of moments(Nc or M): the order of Chebyshev polynomial. The larger Nc, more accurate is the algorithm. Moreover the complexity of the algorithm is $O(DN_c)$, where $D$ is the dimension of the Hamiltonian.

The number of initial vectors(ave):
Since the algorithm needs a random vector as input, taking an average of the several vectors can eliminate the effect of the randomness.
The larger the system is, the smaller effect of randomness is.
And Increasing the number of vectors will not improve the accuracy of the algorithm.

Example

Here are two examples show the effect of Nc and ave. The system is a hamiltonian of size 6564*6564.
vsAve.png

Kpm Dos vs Exact Dos
vsReal.png

标签: Julia

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