Propagators and associated diagrammatic equations are the bedrock upon which a large portion of qunatum many-body theory is built. For one-particle physics, the imaginary-time axis combined with recently developed, maximally compact intermediate representation (IR) allows fast and stable computations. However, in capturing fluctuations and phase transitions, the two-particle propagator takes center stage. It not only encodes more information, but due to the Pauli principle, it is non-trivial to store compactly.
With the recent advent of the overcomplete IR for two-particle quantities and the associated sparse frequency grid for the storage, we are now frequently able to compress the complete three-frequency dependence of two-particle quantities into less than one megabyte of data. In this contribution, we show that sparse time IR grids can also be used to reduce the computational effort of exact diagonalization. We also show that data from numerical renormalization group calculations can similarly be compressed.
Diagrammatic equations at the two-particle level are particularly challenging, as they involve convolutions, which converge slowly. We recently extended the IR approach to we construct small convolution grids that allow for exponentially converging solutions to the Bethe-Salpeter equation.