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

TL;DR

This paper demonstrates that low-rank Green's function representations, specifically the discrete Lehmann representation (DLR), can significantly reduce the Matsubara frequency grid size in dynamical mean-field theory calculations without losing accuracy.

Contribution

The authors show that DLR can replace the full Matsubara grid in DMFT, enabling more efficient computations while maintaining accuracy, demonstrated on Sr$_2$RuO$_4$ at 50K.

Findings

Matsubara quantities can be represented on only 36 DLR nodes.

No loss of accuracy or increase in iterations with DLR grid.

Effective noise handling in Monte Carlo simulations.

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.