Systematically improvable multi-scale solver for correlated electron systems

TL;DR

This paper introduces a hybrid multi-scale solver combining perturbation theory and exact diagonalization, enabling efficient and accurate simulation of strongly correlated electron systems in realistic materials.

Contribution

It presents a novel hybrid method that improves accuracy and efficiency for simulating correlated electrons, avoiding common computational difficulties.

Findings

Accurately models a quantum impurity system with reduced computational cost.

Performs well across various interaction strengths and doping levels.

Avoids issues like double counting and frequency-dependent interactions.

Abstract

The development of numerical methods capable of simulating realistic materials with strongly correlated electrons, with controllable errors, is a central challenge in quantum many-body physics. Here we describe how a hybrid between self-consistent second order perturbation theory and exact diagonalization can be used as a multi-scale solver for such systems. Using a quantum impurity model, generated from a cluster dynamical mean field approximation to the 2D Hubbard model, as a benchmark, we show that our method allows us to obtain accurate results at a fraction of the cost of typical Monte Carlo calculations. We test the behavior of our method in multiple regimes of interaction strengths and doping of the model. The algorithm avoids difficulties such as double counting corrections, frequency dependent interactions, or vertex functions. As it is solely formulated at the level of the single-particle Green's function, it provides a promising route for the simulation of realistic materials that are currently difficult to study with other methods.