Minimax isometry method: A compressive sensing approach for Matsubara summation in many-body perturbation theory
Merzuk Kaltak, Georg Kresse
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 ${\mathrm{SrVO}}_{3}$.
Topics & Concepts
Linear subspaceHilbert spaceLegendre transformationMinimaxIsometry (Riemannian geometry)Compressed sensingPerturbation theory (quantum mechanics)Mathematical analysisPerturbation (astronomy)MathematicsPhysicsQuantum mechanicsPure mathematicsMathematical optimizationAlgorithmAtomic and Subatomic Physics ResearchAdvanced NMR Techniques and ApplicationsQuantum Chromodynamics and Particle Interactions