Non-perturbative approach to nearly antiferromagnetic Fermi liquids

TL;DR

This paper introduces a non-perturbative Monte Carlo method for studying quasiparticles interacting with spin-fluctuations in nearly antiferromagnetic Fermi liquids, avoiding the fermion sign problem and enabling new insights.

Contribution

It develops a novel Monte Carlo approach based on a functional integral over Gaussian fields to analyze spin-fluctuation effects without fermion sign issues.

Findings

Monte Carlo sampling avoids the fermion sign problem.

Results align with perturbative and one-loop calculations.

Provides a new computational tool for strongly correlated systems.

Abstract

We present a non-perturbative approach to the problem of quasiparticles coupled to spin-fluctuations. If the fully dressed spin-fluctuation propagator is used in the Feynman graph expansion of the single-particle Green's function, the problem of summing all spin-fluctuation exchange graphs (i.e without virtual fermion loops) can be cast as a functional integral over gaussian distributed random vector fields. A Monte Carlo sampling of this functional integral does not suffer from the 'fermion sign problem' and offers an attractive alternative to perturbative calculations. We compare the results of our computer simulations with perturbation theory and self-consistent one-loop calculations.