Tracking the Footprints of Spin Fluctuations: A MultiMethod, MultiMessenger Study of the Two-Dimensional Hubbard Model

TL;DR

This study compares various advanced quantum many-body methods to understand spin fluctuations and electronic regimes in the two-dimensional Hubbard model, revealing insights into quasiparticle behavior and magnetic correlations across different temperature regimes.

Contribution

It provides a comprehensive multi-method analysis of the Hubbard model, highlighting the strengths and limitations of each approach in capturing physical regimes and spin fluctuation effects.

Findings

Dynamical mean-field theory accurately approximates local quantities in the metallic regime.

Long-range antiferromagnetic correlations coexist with quasiparticles.

Imaginary time methods may struggle to capture non-Fermi liquid singularities.

Abstract

The Hubbard model represents the fundamental model for interacting quantum systems and electronic correlations. Using the two-dimensional half-filled Hubbard model at weak coupling as a testing ground, we perform a comparative study of a comprehensive set of state of the art quantum many-body methods. Upon cooling into its insulating antiferromagnetic ground-state, the model hosts a rich sequence of distinct physical regimes with crossovers between a high-temperature incoherent regime, an intermediate temperature metallic regime and a low-temperature insulating regime with a pseudogap created by antiferromagnetic fluctuations. We assess the ability of each method to properly address these physical regimes and crossovers through the computation of several observables probing both quasiparticle properties and magnetic correlations, with two numerically exact methods (diagrammatic and determinantal quantum Monte Carlo) serving as a benchmark. By combining computational results and analytical insights, we elucidate the nature and role of spin fluctuations in each of these regimes. Based on this analysis, we explain how quasiparticles can coexist with increasingly long-range antiferromagnetic correlations, and why dynamical mean-field theory is found to provide a remarkably accurate approximation of local quantities in the metallic regime. We also critically discuss whether imaginary time methods are able to capture the non-Fermi liquid singularities of this fully nested system.