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

摘要

The popular, stable, robust and computationally inexpensive cubic splineinterpolation algorithm is adopted and used for finite temperature Green'sfunction calculations of realistic systems. We demonstrate that withappropriate modifications the temperature dependence can be preserved while theGreen's function grid size can be reduced by about two orders of magnitude byreplacing the standard Matsubara frequency grid with a sparser grid and a setof interpolation coefficients. We benchmarked the accuracy of our algorithm asa function of a single parameter sensitive to the shape of the Green'sfunction. Through numerous examples, we confirmed that our algorithm can beutilized in a systematically improvable, controlled, and black-box manner andhighly accurate one- and two-body energies and one-particle density matricescan 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 ofgrid points needs to be doubled, whereas for the Matsubara frequency grid anorder of magnitude more grid points must be used. This suggests that realisticcalculations with large basis sets that were previously out of reach becausethey required enormous grid sizes may now become feasible.