Sparse sampling approach to efficient <i>ab initio</i> calculations at finite temperature

Abstract

Efficient ab initio calculations of correlated materials at finite temperatures require compact representations of the Green's functions both in imaginary time and in Matsubara frequency. In this paper, we introduce a general procedure which generates sparse sampling points in time and frequency from compact orthogonal basis representations, such as Chebyshev polynomials and intermediate representation basis functions. These sampling points accurately resolve the information contained in the Green's function, and efficient transforms between different representations are formulated with minimal loss of information. As a demonstration, we apply the sparse sampling scheme to diagrammatic $GW$ and second-order Green's function theory calculations of a hydrogen chain of noble gas atoms and of a silicon crystal.