Chin. Phys. B, 2022, Vol. 31(5): 050203    DOI: 10.1088/1674-1056/ac5986
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# 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
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.
Keywords:  exact diagonalization      Lanczos method      orthogonal polynomials
Received:  12 January 2022      Revised:  15 February 2022      Accepted manuscript online:
 PACS: 02.60.Dc (Numerical linear algebra) 02.60.-x (Numerical approximation and analysis) 75.10.Jm (Quantized spin models, including quantum spin frustration) 75.40.Mg (Numerical simulation studies)
Fund: 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).
Corresponding Authors:  Hai-Qing Lin,E-mail:haiqing0@csrc.ac.cn     E-mail:  haiqing0@csrc.ac.cn
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