Kernel polynomial representation for imaginary-time Green's functions in continuous-time quantum Monte Carlo impurity solver

Inspired by the recently proposed Legendre orthogonal polynomial representation for imaginary-time Green's functions G(τ), we develop an alternate and superior representation for G(τ) and implement it in the hybridization expansion continuous-time quantum Monte Carlo impurity solver. This representation is based on the kernel polynomial method, which introduces some integral kernel functions to filter the numerical fluctuations caused by the explicit truncations of polynomial expansion series and can improve the computational precision significantly. As an illustration of the new representation, we re-examine the imaginary-time Green's functions of the single-band Hubbard model in the framework of dynamical mean-field theory. The calculated results suggest that with carefully chosen integral kernel functions, whether the system is metallic or insulating, the Gibbs oscillations found in the previous Legendre orthogonal polynomial representation have been vastly suppressed and remarkable corrections to the measured Green's functions have been obtained.