The Hubbard model in the two-pole approximation

TL;DR

This paper analyzes the two-dimensional Hubbard model using a two-pole expansion, revealing equivalences among theoretical approaches and emphasizing the importance of the Pauli principle and symmetry properties.

Contribution

It demonstrates the equivalence of various low-level theoretical methods and introduces a unique way to preserve key physical principles in the Hubbard model analysis.

Findings

Different methods are equivalent at their lowest level

Preserving the Pauli principle is crucial for accurate results

A comparison with quantum Monte Carlo data validates the approach

Abstract

The two-dimensional Hubbard model is analyzed in the framework of the two-pole expansion. It is demonstrated that several theoretical approaches, when considered at their lowest level, are all equivalent and share the property of satisfying the conservation of the first four spectral momenta. It emerges that the various methods differ only in the way of fixing the internal parameters and that it exists a unique way to preserve simultaneously the Pauli principle and the particle-hole symmetry. A comprehensive comparison with respect to some general symmetry properties and the data from quantum Monte Carlo analysis shows the relevance of imposing the Pauli principle.