Distributional exact diagonalization formalism for quantum impurity models

TL;DR

This paper introduces a stochastic distributional approach for calculating the self-energy of quantum impurity models, enabling accurate real-frequency data without analytic continuation.

Contribution

The authors develop a novel method that uses stochastic sampling of finite Anderson models to compute the self-energy directly on the real frequency axis.

Findings

Good agreement with quantum Monte Carlo data

Accurate real-frequency self-energy calculations

Applicable to various impurity models

Abstract

We develop a method for calculating the self-energy of a quantum impurity coupled to a continuous bath by stochastically generating a distribution of finite Anderson models that are solved by exact diagonalization, using the noninteracting local spectral function as a probability distribution for the sampling. The method enables calculation of the full analytic self-energy and single-particle Green's function in the complex frequency plane, without analytic continuation, and can be used for both finite and zero temperature at arbitrary fillings. Results are in good agreement with imaginary frequency data from continuous-time quantum Monte Carlo calculations for the single impurity Anderson model and the two-orbital Hubbard model within dynamical mean field theory (DMFT) as well as real frequency data for self energy of the single band Hubbard model within DMFT using numerical renormalization group. The method should be applicable to a wide range of quantum impurity models and particularly useful when high-precision real frequency results are sought.