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.

5 pages, 4 figures

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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