Minimax Isometry Method: A compressive sensing approach for Matsubara summation in many-body perturbation theory

TL;DR

This paper introduces a compressive sensing method to efficiently perform Matsubara summation in many-body perturbation theory, enabling data compression and accurate calculations across various temperatures.

Contribution

It develops a novel isometry-based approach to optimize imaginary time and frequency grids for better data compression in quantum many-body calculations.

Findings

Effective data compression for fermionic and bosonic functions.

Accurate results demonstrated for Si and SrVO$_3$.

Applicable to RPA and GW approximations.

Abstract

We present a compressive sensing approach for the long standing problem of Matsubara summation in many-body perturbation theory. By constructing low-dimensional, almost isometric subspaces of the Hilbert space we obtain optimum imaginary time and frequency grids that allow for extreme data compression of fermionic and bosonic functions in a broad temperature regime. The method is applied to the random phase and self-consistent $GW$ approximation of the grand potential. Integration and transformation errors are investigated for Si and SrVO$_3$.