Multi-scale Extensions to Quantum Cluster Methods for Strongly Correlated Electron Systems

TL;DR

This paper introduces a multi-scale approach to quantum cluster methods for strongly correlated electrons, combining explicit, mean-field, and diagrammatic treatments across different length-scales, validated on the 1D Hubbard model.

Contribution

It presents a novel multi-scale extension to quantum cluster methods that efficiently approximates correlations across various length-scales in strongly correlated systems.

Findings

Achieves good quantitative agreement with Quantum Monte-Carlo results.

Effectively treats short, intermediate, and long-range correlations.

Reduces computational cost compared to fully explicit methods.

Abstract

A numerically implementable Multi-scale Many-Body approach to strongly correlated electron systems is introduced. An extension to quantum cluster methods, it approximates correlations on any given length-scale commensurate with the strength of the correlations on the respective scale. Short length-scales are treated explicitly, long ones are addressed at a mean-field level and intermediate length-regime correlations are assumed to be weak and are approximated diagrammatically. To illustrate and test this method, we apply it to the one dimensional Hubbard model. The resulting multi-scale self-energy provides a very good quantitative agreement with substantially more numerically expensive, explicit Quantum Monte-Carlo calculations.