Efficient temperature-dependent Green's function methods for realistic systems: using cubic spline interpolation to approximate Matsubara Green's functions

TL;DR

This paper introduces a cubic spline interpolation method for finite temperature Green's function calculations that significantly reduces computational cost while maintaining high accuracy, enabling feasible large-scale realistic system simulations.

Contribution

The authors develop a modified cubic spline interpolation approach that preserves temperature dependence and drastically reduces grid size for Green's function calculations.

Findings

Green's function grid size reduced by about 98%.

High accuracy achieved with only 5% of original grid points.

Order of magnitude improvement in computational efficiency.

Abstract

The popular, stable, robust and computationally inexpensive cubic spline interpolation algorithm is adopted and used for finite temperature Green's function calculations of realistic systems. We demonstrate that with appropriate modifications the temperature dependence can be preserved while the Green's function grid size can be reduced by about two orders of magnitude by replacing the standard Matsubara frequency grid with a sparser grid and a set of interpolation coefficients. We benchmarked the accuracy of our algorithm as a function of a single parameter sensitive to the shape of the Green's function. Through numerous examples, we confirmed that our algorithm can be utilized in a systematically improvable, controlled, and black-box manner and highly accurate one- and two-body energies and one-particle density matrices can be obtained using only around 5% of the original grid points. Additionally, we established that to improve accuracy by an order of magnitude, the number of grid points needs to be doubled, whereas for the Matsubara frequency grid an order of magnitude more grid points must be used. This suggests that realistic calculations with large basis sets that were previously out of reach because they required enormous grid sizes may now become feasible.