Efficient ab initio many-body calculations based on sparse modeling of Matsubara Green's function

Abstract

This lecture note reviews recently proposed sparse-modeling approaches for efficient ab initio many-body calculations based on the data compression of Green's functions. The sparse-modeling techniques are based on a compact orthogonal basis, an intermediate representation (IR) basis, for imaginary-time and Matsubara Green's functions. A sparse sampling method based on the IR basis enables solving diagrammatic equations efficiently. We describe the basic properties of the IR basis, the sparse sampling method and its applications to ab initio calculations based on the GW approximation and the Migdal-Eliashberg theory. We also describe a numerical library for the IR basis and the sparse sampling method, sparse-ir, and provide its sample codes. This lecture note follows the Japanese review article with major revisions [H. Shinaoka et al., Solid State Physics 56(6), 301 (2021)].

29 pages, 11 figures

References in corpus (5)

• Dynamical vertex approximation - a step beyond dynamical mean field theory
• Cubic scaling $GW$: towards fast quasiparticle calculations
• Discrete Lehmann representation of imaginary time Green's functions
• Sparse Modeling in Quantum Many-Body Problems
• Doping fingerprints of spin and lattice fluctuations in moiré superlattice systems

Cited by in corpus (25)

• Quenched pair breaking by interlayer correlations as a key to superconductivity in La${}_3$Ni${}_2$O${}_7$
• Discrete Lehmann representation of imaginary time Green's functions
• sparse-ir: optimal compression and sparse sampling of many-body propagators
• Multiscale space-time ansatz for correlation functions of quantum systems based on quantics tensor trains
• Bosonic Nevanlinna Analytic Continuation
• Two-particle correlations and the metal-insulator transition: Iterated Perturbation Theory revisited
• A fast time domain solver for the equilibrium Dyson equation
• Minimal Pole Representation and Controlled Analytic Continuation of Matsubara Response Functions
• Challenges with relativistic GW calculations in solids and molecules
• No superconductivity in Pb${}_9$Cu${}_1$(PO${}_4$)${}_6$O found in orbital and spin fluctuation exchange calculations
• Compactness of quantics tensor train representations of local imaginary-time propagators
• Efficient anisotropic Migdal-Eliashberg calculations with the Intermediate Representation basis and Wannier interpolation
• Decomposing imaginary time Feynman diagrams using separable basis functions: Anderson impurity model strong coupling expansion
• Doping fingerprints of spin and lattice fluctuations in moiré superlattice systems
• Quasiparticle and fully self-consistent GW methods: an unbiased analysis using Gaussian orbitals
• Low-rank quantics tensor train representations of Feynman diagrams for multiorbital electron-phonon models
• Stabilizing the calculation of the self-energy in dynamical mean-field theory using constrained residual minimization
• Compressing the two-particle Green's function using wavelets: Theory and application to the Hubbard atom
• Overcomplete intermediate representation of two-particle Green's functions and its relation to partial spectral functions
• Tensor cross interpolation approach for quantum impurity problems based on the weak-coupling expansion
• Supercurrent-induced antiferromagnetic order and spin-triplet pair generation in quantum critical d-wave superconductors
• Computation Kernel for Feynman Diagrams
• Spin liquid phase in the Hubbard model: Luttinger-Ward analysis of the slave-rotor formalism
• Uniform electron benchmark for the first-principles $G{W}_0$-Eliashberg theory
• Local-moment magnetism in Mn-based pnictides