Physics

Linear subspace

Perturbation (astronomy)

Pure mathematics

Mathematics

Algorithm

Mathematical optimization

Legendre transformation

Compressed sensing

Mathematical analysis

Minimax

Perturbation theory (quantum mechanics)

Quantum mechanics

Hilbert space

Isometry (Riemannian geometry)

Physical review. B./Physical review. B

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$_3$.

Minimax isometry method: A compressive sensing approach for Matsubara summation in many-body perturbation theory