Sparse sampling approach to efficient ab initio calculations at finite temperature

TL;DR

This paper introduces a sparse sampling method for efficient finite-temperature ab initio calculations, enabling accurate Green's function representations with fewer sampling points, demonstrated on various materials.

Contribution

It presents a general procedure for generating sparse sampling points from orthogonal basis representations, improving efficiency in ab initio finite-temperature calculations.

Findings

Accurate Green's function resolution with fewer sampling points

Efficient transforms between time and frequency representations

Successful application to hydrogen chain, noble gases, and silicon crystal

Abstract

Efficient ab initio calculations of correlated materials at finite temperature require compact representations of the Green's functions both in imaginary time and 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 (IR) 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 GF2 calculations of a hydrogen chain, of noble gas atoms and of a silicon crystal.