Partial Renormalization of Quasiparticle Interactions

TL;DR

This paper introduces a projection-based renormalization scheme for nonlocal interactions in quantum many-body systems, enabling efficient and predictive perturbative calculations even in strongly correlated regimes.

Contribution

It presents a novel renormalization approach that selectively resums key nonlocal contributions, simplifying the treatment of complex effective interactions in many-body perturbation theory.

Findings

The method remains predictive in strongly correlated regimes.

Significant sign cancellations are observed between scattering channels.

Efficient computation using diagrammatic Monte Carlo is demonstrated.

Abstract

Nonlocal effective interactions are inherent to non-relativistic quantum many-body systems, but their systematic resummation poses a significant challenge known as the ``vertex problem" in many-body perturbation theory. We introduce a renormalization scheme based on a projection-based renormalization condition that selectively resums the most essential nonlocal contributions to the effective interaction vertex, avoiding the computational complexity of the full vertex function. This enables us to derive a renormalized Feynman diagrammatic series with large parameters canceled by counter-diagrams, efficiently generated using a perturbative expansion of the parquet equations and computed using a diagrammatic Monte Carlo algorithm. Applying our approach to a 3D Yukawa Fermi liquid, we demonstrate that the renormalized perturbation theory remains predictive even in the strongly correlated regime and uncover significant sign cancellations between different channels contributing to the scattering amplitude. Our work establishes a novel framework for investigating strong correlations in quantum many-body systems, offering a systematic approach to explore nonlocal theories for challenging systems like the electron liquid in material science.