Doping induced metal-insulator transition in two-dimensional Hubbard, $t-U$, and extended Hubbard, $t-U-W$, models

TL;DR

This study numerically investigates how adding a W-dependent term to the 2D Hubbard model changes the doping-induced metal-insulator transition, revealing a transition to a d-wave superconductor.

Contribution

It demonstrates that the inclusion of the W term fundamentally alters the critical behavior of the metal-insulator transition in the 2D Hubbard model.

Findings

Localization length scales as |μ - μ_c|^{-1/2} with W

Localization length scales as |μ - μ_c|^{-1/4} in the Hubbard model

Doping leads to a d_{x^2 - y^2} superconductor with finite W

Abstract

We show numerically that the nature of the doping induced metal-insulator transition in the two-dimensional Hubbard model is radically altered by the inclusion of a term, $W$, which depends upon a square of a single-particle nearest-neighbor hopping. This result is reached by computing the localization length, $\xi_l$, in the insulating state. At finite values of $W$ we find results consistent with $\xi_l \sim | \mu - \mu_c|^{- 1/2} $ where $\mu_c$ is the critical chemical potential. In contrast, $\xi_l \sim | \mu - \mu_c|^{-1/4}$ for the Hubbard model. At finite values of $W$, the presented numerical results imply that doping the antiferromagnetic Mott insulator leads to a $d_{x^2 - y ^2}$ superconductor.