Gauss quadrature based finite temperature Lanczos method

doi:10.1088/1674-1056/ac5986

中国物理B ›› 2022, Vol. 31 ›› Issue (5): 50203-050203.doi: 10.1088/1674-1056/ac5986

Gauss quadrature based finite temperature Lanczos method

Jian Li(李健) and Hai-Qing Lin(林海青)^†

Beijing Computational Science Research Center, Beijing 100193, China

收稿日期:2022-01-12 修回日期:2022-02-15 出版日期:2022-05-14 发布日期:2022-05-05
通讯作者: Hai-Qing Lin,E-mail:haiqing0@csrc.ac.cn E-mail:haiqing0@csrc.ac.cn
基金资助:
This work is supported by the National Natural Science Foundation of China (Grant Nos.11734002 and U1930402).All numerical computations were carried out on the Tianhe-2JK at the Beijing Computational Science Research Center (CSRC).

Gauss quadrature based finite temperature Lanczos method

Jian Li(李健) and Hai-Qing Lin(林海青)^†

Beijing Computational Science Research Center, Beijing 100193, China

Received:2022-01-12 Revised:2022-02-15 Online:2022-05-14 Published:2022-05-05
Contact: Hai-Qing Lin,E-mail:haiqing0@csrc.ac.cn E-mail:haiqing0@csrc.ac.cn
About author:2022-3-2
Supported by:
This work is supported by the National Natural Science Foundation of China (Grant Nos.11734002 and U1930402).All numerical computations were carried out on the Tianhe-2JK at the Beijing Computational Science Research Center (CSRC).

摘要/Abstract

摘要： The finite temperature Lanczos method (FTLM), which is an exact diagonalization method intensively used in quantum many-body calculations, is formulated in the framework of orthogonal polynomials and Gauss quadrature. The main idea is to reduce finite temperature static and dynamic quantities into weighted summations related to one- and two-dimensional Gauss quadratures. Then lower order Gauss quadrature, which is generated from Lanczos iteration, can be applied to approximate the initial weighted summation. This framework fills the conceptual gap between FTLM and kernel polynomial method, and makes it easy to apply orthogonal polynomial techniques in the FTLM calculation.

关键词: exact diagonalization, Lanczos method, orthogonal polynomials

Abstract: The finite temperature Lanczos method (FTLM), which is an exact diagonalization method intensively used in quantum many-body calculations, is formulated in the framework of orthogonal polynomials and Gauss quadrature. The main idea is to reduce finite temperature static and dynamic quantities into weighted summations related to one- and two-dimensional Gauss quadratures. Then lower order Gauss quadrature, which is generated from Lanczos iteration, can be applied to approximate the initial weighted summation. This framework fills the conceptual gap between FTLM and kernel polynomial method, and makes it easy to apply orthogonal polynomial techniques in the FTLM calculation.

Key words: exact diagonalization, Lanczos method, orthogonal polynomials

中图分类号: (Numerical linear algebra)

02.60.Dc

02.60.-x (Numerical approximation and analysis) 75.10.Jm (Quantized spin models, including quantum spin frustration) 75.40.Mg (Numerical simulation studies)

Jian Li(李健) and Hai-Qing Lin(林海青). Gauss quadrature based finite temperature Lanczos method[J]. 中国物理B, 2022, 31(5): 50203-050203.

Jian Li(李健) and Hai-Qing Lin(林海青). Gauss quadrature based finite temperature Lanczos method[J]. Chin. Phys. B, 2022, 31(5): 50203-050203.

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Gauss quadrature based finite temperature Lanczos method

Gauss quadrature based finite temperature Lanczos method

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