A Nonperturbative Approach to One-Particle Green's Function

TL;DR

This paper introduces a nonperturbative method for calculating one-particle Green's functions, demonstrating its effectiveness on Hubbard models and revealing insights into metal-insulator transitions.

Contribution

The paper presents a novel nonperturbative approach for Green's functions applicable to complex Hubbard models, outperforming traditional continued fraction methods.

Findings

Method successfully applied to noninteracting and interacting Hubbard models

Reveals metal-insulator transition via on-site spin fluctuations

Demonstrates advantages over existing formalism

Abstract

A nonperturbative method to obtain on- and off-site one-particle Green's function is introduced and applied to noninteracting Hubbard model with next nearest neighbor hopping and interacting Hubbard model in large dimensions, for example. The former gives some lessons on the method and shows the advantage of the method compared with continued fraction formalism. The latter is treated by selecting important dynamic processes contributing to the Green's function when correlation is strong. We consider the model in the Bethe lattice with large connectivity. The dynamic processes describing on-site spin fluctuation clearly shows metal-insulator transition in the paramagnetic ground state at half filling.