Minimax Isometry Method: A Compressive Sensing Approach For Matsubara Summation In Many-Body Perturbation Theory

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 selfconsistent GW approximation of the grand potential. Integration and transformation errors are investigated for Si and SrVO3.