Kernel polynomial representation of imaginary-time Green's functions

TL;DR

This paper introduces a kernel polynomial method for representing imaginary-time Green's functions in quantum impurity models, significantly reducing oscillations and improving computational accuracy in dynamical mean-field theory calculations.

Contribution

It develops an alternative kernel polynomial representation that suppresses Gibbs oscillations and enhances precision in Green's function computations within quantum impurity models.

Findings

Suppression of Gibbs oscillations using kernel functions

Enhanced accuracy of Green's functions in Hubbard model

Improved computational stability in quantum Monte Carlo simulations

Abstract

Inspired by the recent proposed Legendre orthogonal polynomial representation of imaginary-time Green's functions, we develop an alternate representation for the Green's functions of quantum impurity models and combine it with the hybridization expansion continuous-time quantum Monte Carlo impurity solver. This representation is based on the kernel polynomial method, which introduces various integral kernels to filter fluctuations caused by the explicit truncations of polynomial expansion series and improve the computational precision significantly. As an illustration of the new representation, we reexamine the imaginary-time Green's functions of single-band Hubbard model in the framework of dynamical mean-field theory. The calculated results suggest that with carefully chosen integral kernels the Gibbs oscillations found in previous orthogonal polynomial representation have been suppressed vastly and remarkable corrections to the measured Green's functions have been obtained.