Strong-Coupling Perturbation Theory of the Hubbard Model

TL;DR

This paper develops a high-order strong-coupling perturbation theory for the Hubbard model, providing detailed analytical results, comparisons with Monte Carlo data, and exploring different physical regimes across various parameters.

Contribution

It introduces a comprehensive strong-coupling perturbation framework for the Hubbard model, including higher-order calculations and extensions beyond half-filling.

Findings

Spectral weight A(k,omega) expressed as a Jacobi continued fraction

Identification of insulator, conductor, and antiferromagnetic regimes in the T-t plane

Good agreement with Monte Carlo data in one-dimensional case

Abstract

The strong-coupling perturbation theory of the Hubbard model is presented and carried out to order (t/U)^5 for the one-particle Green function in arbitrary dimension. The spectral weight A(k,omega) is expressed as a Jacobi continued fraction and compared with new Monte-Carlo data of the one-dimensional, half-filled Hubbard model. Different regimes (insulator, conductor and short-range antiferromagnet) are identified in the temperature--hopping integral (T,t) plane. This work completes a first paper on the subject (Phys. Rev. Lett. 80, 5389 (1998)) by providing details on diagrammatic rules and higher-order results. In addition, the non half-filled case, infinite resummations of diagrams and the double occupancy are discussed. Various tests of the method are also presented.