Precursors of Antiferromagnetic and Hubbard Bands in the 2D Hubbard Model

TL;DR

This paper develops a finite-size effect-free theoretical framework for the 2D Hubbard model, revealing how critical fluctuations and increasing interaction strength lead to characteristic spectral features like split peaks and band formations.

Contribution

It introduces a novel theoretical approach that captures essential 2D Hubbard model features without finite size effects or numerical continuation, highlighting the emergence of spectral peaks and bands.

Findings

Critical fluctuations cause a split peak in spectral function at low temperatures.

Increasing U leads to the development of antiferromagnetic and Hubbard bands.

The theory accurately reproduces atomic limit behavior at high frequencies.

Abstract

We formulate a theory to the 2D Hubbard model in a framework free of finite size effect and numerical analytical continuation, yet containing the essential features of the 2D Hubbard model, i.e., the correct atomic limit for large frequencies and 2D spin fluctuations. As temperature is decreased for a 2D half-filled band, 2D critical fluctuations give rise to a strong local maximum in the scattering rates at the chemical potential leading to a split peak in the spectral function. As U is increased, four peaks associated with antiferromagnetic and Hubbard bands begin to develop in small and intermediate frequency regimes.