Metal-Insulator Transition in the Two-Dimensional Hubbard Model at Half-Filling with Lifetime Effects within the Moment Approach

TL;DR

This paper investigates the metal-insulator transition in the 2D Hubbard model at half-filling, incorporating lifetime effects via the moment approach, revealing a Mott transition at realistic interaction strengths and emphasizing the importance of lifetime effects.

Contribution

It introduces a method to include lifetime effects in the moment approach for the Hubbard model, improving the understanding of the Mott transition without artificial gaps.

Findings

Identifies a Mott transition at U/W ≥ 1 consistent with numerical results.

Shows lifetime effects are crucial for accurate modeling of the transition.

Demonstrates the method's superiority over previous approximations.

Abstract

We explore the effect of the imaginary part of the self-energy, $Im\Sigma(\vec{k},\omega)$, having a single pole, $\Omega(\vec{k},\omega)$, with spectral weight, $\alpha(\vec{k})$, and quasi-particle lifetime, $\Gamma(\vec{k})$, on the density of states. We solve the set of parameters, $\Omega(\vec{k},\omega$), $\alpha(\vec{k})$, and $\Gamma(\vec{k})$ by means of the moment approach (exact sum rules) of Nolting. Our choice for $\Sigma(k,\omega)$, satisfies the Kramers - Kronig relationship automatically. Due to our choice of the self - energy, the system is not a Fermi liquid for any value of the interaction, a result which is also true in the moment approach of Nolting without lifetime effects. By increasing the value of the local interaction, $U/W$, at half-filling ($\rho = 1/2$), we go from a paramagnetic metal to a paramagnetic insulator, (Mott metal - insulator transition ($MMIT$)) for values of $U/W$ of the order of $U/W \geq 1$ ($W$ is the band width) which is in agreement with numerical results for finite lattices and for infinity dimensions ($D = \infty$). These results settle down the main weakness of the spherical approximation of Nolting: a finite gap for any finite value of the interaction, i.e., an insulator for any finite value of $U/W$. Lifetime effects are absolutely indispensable. Our scheme works better than the one of improving the narrowing band factor, $B(\vec{k})$, beyond the spherical approximation of Nolting.