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

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${}_3$.

arXiv comment19 pages, 11 figures

References in corpus (12)

• Orthogonal Polynomial Representation of Imaginary-Time Green's Functions
• Predictive GW calculations using plane waves and pseudopotentials
• The Band-Gap Problem in Semiconductors Revisited: Effects of Core States and Many-Body Self-Consistency
• The GW space-time method for the self-energy of large systems
• Compressing Green's function using intermediate representation between imaginary-time and real-frequency domains
• Cubic scaling $GW$: towards fast quasiparticle calculations
• Sparse sampling approach to efficient ab initio calculations at finite temperature
• Bond Breaking and Bond Formation: How Electron Correlation is Captured in Many-Body Perturbation Theory and Density-Functional Theory
• Beyond the quasiparticle approximation: Fully self-consistent $GW$ calculations
• Ground State Properties of Simple Elements from GW Calculations
• Exploring connections between statistical mechanics and Green's functions for realistic systems. Temperature dependent electronic entropy and internal energy from a self-consistent second-order Green's function
• Kernel polynomial representation of imaginary-time Green's functions

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• New insights into the 1D carbon chain through the RPA
• Complex Absorbing Potential Green's Function Methods for Resonances
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• Heating and cooling in self-consistent many-body simulations
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