Gauss quadrature based finite temperature Lanczos method

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.