Non-perturbative many-body approach to the Hubbard model and single-particle pseudogap

TL;DR

This paper introduces a non-perturbative, conserving many-body approach to the Hubbard model that accurately captures spin fluctuations, pseudogap phenomena, and respects fundamental physical principles, aligning well with Monte Carlo results.

Contribution

It presents a novel self-consistent method enforcing conservation laws and sum-rules, providing a quantitative framework for understanding pseudogap and spin fluctuation effects in the Hubbard model.

Findings

Quantitative agreement with Monte Carlo simulations.

Observation of precursors to antiferromagnetic bands.

Destruction of Fermi-liquid quasiparticles in 2D above zero-temperature transition.

Abstract

A new approach to the single-band Hubbard model is described in the general context of many-body theories. It is based on enforcing conservation laws, the Pauli principle and a number of crucial sum-rules. More specifically, spin and charge susceptibilities are expressed, in a conserving approximation, as a function of two constant irreducible vertices whose values are found self-consistently. The Mermin-Wagner theorem in two dimensions is automatically satisfied. The effect of collective modes on single-particle properties is then obtained by a paramagnon-like formula that is consistent with the two-particle properties in the sense that the potential energy obtained from $Tr\Sigma G$ is identical to that obtained using the fluctuation-dissipation theorem for susceptibilities. The vertex corrections are included through constant irreducible vertices. The theory is in quantitative agreement with Monte Carlo simulations for both single-particle and two-particle properties. In the two-dimensional renormalized classical regime, spin fluctuations lead to precursors of antiferromagnetic bands (shadow bands) and to the destruction of the Fermi-liquid quasiparticles in a wide temperature range above the zero-temperature phase transition. The analogous phenomenon of pairing pseudogap can occur in the attractive model in two dimensions when the pairing fluctuations become critical. Other many-body approaches are critically compared. It is argued that treating the spin fluctuations as if there was a Migdal's theorem can lead to wrong predictions, in particular with regard to the the single-particle pseudogap.