2017年
Reduced-Shifted Conjugate-Gradient Method for a Green's Function: Efficient Numerical Approach in a Nano-Structured Superconductor
Journal of the Physical Society of Japan
- ,
- ,
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- 巻
- 86
- 号
- 1
- 開始ページ
- 014708
- 終了ページ
- 記述言語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.7566/JPSJ.86.014708
- 出版者・発行元
- The Physical Society of Japan
© 2017 The Physical Society of Japan.We propose the reduced-shifted conjugate-gradient (RSCG) method, which is numerically efficient to calculate a matrix element of a Green's function defined as a resolvent of a Hamiltonian operator, by solving linear equations with a desired accuracy. This method does not calculate solution vectors of linear equations but does directly calculate a matrix element of the resolvent. The matrix elements with different frequencies are simultaneously obtained. Thus, it is easy to calculate the exception value expressed as a Matsubara summation of these elements. To illustrate a power of our method, we choose a nano-structured superconducting system with a mean-field Bogoliubov-de Gennes (BdG) approach. This method allows us to treat with the system with the fabrication potential, where one cannot effectively use the kernel-polynomial-based method. We consider the d-wave nano-island superconductor by simultaneously solving the linear equations with a large number (∼50000) of Matsubara frequencies.
- リンク情報
- ID情報
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- DOI : 10.7566/JPSJ.86.014708
- ISSN : 0031-9015
- ORCIDのPut Code : 30821959
- SCOPUS ID : 85007475035
- Web of Science ID : WOS:000391858100026