Low rank Green's function representations applied to dynamical mean-field theory

Abstract

Several recent works have introduced highly compact representations of single-particle Green's functions in the imaginary time and Matsubara frequency domains, as well as efficient interpolation grids used to recover the representations. In particular, the intermediate representation with sparse sampling and the discrete Lehmann representation (DLR) make use of low-rank compression techniques to obtain optimal approximations with controllable accuracy. We consider the use of the DLR in dynamical mean-field theory (DMFT) calculations, and in particular, show that the standard full Matsubara frequency grid can be replaced by the compact grid of DLR Matsubara frequency nodes. We test the performance of the method for a DMFT calculation of Sr${}_2$RuO${}_4$ at temperature $50$K using a continuous-time quantum Monte Carlo impurity solver, and demonstrate that Matsubara frequency quantities can be represented on a grid of only $36$ nodes with no reduction in accuracy, or increase in the number of self-consistent iterations, despite the presence of significant Monte Carlo noise.

arXiv comment5 pages, 4 figures

References in corpus (25)

• Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials
• Wannier90: A Tool for Obtaining Maximally-Localised Wannier Functions
• Electronic Structure Calculations with Dynamical Mean-Field Theory: A Spectral Density Functional Approach
• Pseudopotentials for high-throughput DFT calculations
• Strong electronic correlations from Hund's coupling
• TRIQS: A Toolbox for Research on Interacting Quantum Systems
• TRIQS/CTHYB: A Continuous-Time Quantum Monte Carlo Hybridization Expansion Solver for Quantum Impurity Problems
• Orthogonal Polynomial Representation of Imaginary-Time Green's Functions
• The Band-Gap Problem in Semiconductors Revisited: Effects of Core States and Many-Body Self-Consistency
• Compressing Green's function using intermediate representation between imaginary-time and real-frequency domains
• Sparse sampling approach to efficient ab initio calculations at finite temperature
• Discrete Lehmann representation of imaginary time Green's functions
• New Evidence for a Low-Temperature Magnetic Ground State in Double-Perovskite Iridates with Ir5+(5d4) Ions
• sparse-ir: optimal compression and sparse sampling of many-body propagators
• Efficient temperature-dependent Green's functions methods for realistic systems: compact grids for orthogonal polynomial transforms
• Chebyshev polynomial representation of imaginary time response functions
• Fully Self-Consistent Finite-Temperature $GW$ in Gaussian Bloch Orbitals for Solids
• Performance analysis of a physically constructed orthogonal representation of imaginary-time Green's function
• Minimax Isometry Method: A compressive sensing approach for Matsubara summation in many-body perturbation theory
• Legendre-spectral Dyson equation solver with super-exponential convergence
• libdlr: Efficient imaginary time calculations using the discrete Lehmann representation
• Solving the Bethe-Salpeter equation with exponential convergence
• Efficient ab initio Migdal-Eliashberg calculation considering the retardation effect in phonon-mediated superconductors
• Superconductivity in the Uniform Electron Gas: Irrelevance of Kohn-Luttinger Mechanism
• Sparse modeling approach for quasiclassical theory of superconductivity

Cited by in corpus (6)

• Decomposing imaginary time Feynman diagrams using separable basis functions: Anderson impurity model strong coupling expansion
• Quasiparticle and fully self-consistent GW methods: an unbiased analysis using Gaussian orbitals
• Stabilizing the calculation of the self-energy in dynamical mean-field theory using constrained residual minimization
• Discrete Lehmann representation of three-point functions
• cppdlr: Imaginary time calculations using the discrete Lehmann representation
• Automated evaluation of imaginary time strong coupling diagrams by sum-of-exponentials hybridization fitting