Embedded multi-boson exchange: A step beyond quantum cluster theories

TL;DR

This paper presents a novel multi-scale diagrammatic approach for the Hubbard model that effectively captures both short- and long-range correlations, improving upon existing quantum cluster theories.

Contribution

It introduces a multi-boson exchange framework that combines cluster vertices with diagrammatic equations, resolving interaction ambiguities and aligning well with exact simulations.

Findings

Excellent agreement with diagrammatic Monte Carlo results

Accurate capture of short- and long-range correlations

Resolves Fierz ambiguity exactly

Abstract

We introduce a diagrammatic multi-scale approach to the Hubbard model based on the interaction-irreducible (multi-boson) vertex of a small cluster embedded in a self-consistent medium. The vertex captures short-ranged correlations up to the length scale of the cluster, while long-ranged correlations are recovered from a set of diagrammatic equations for the Hedin three-leg vertex. By virtue of the crossing symmetry, the Fierz decoupling ambiguity of the Hubbard interaction is resolved exactly. Our benchmarks for the half-filled Hubbard model on the square lattice are in very good agreement with numerically exact diagrammatic Monte Carlo simulations.