Metal-insulator transition in (2+1)-dimensional Hubbard model with tensor renormalization group

TL;DR

This study uses tensor renormalization group methods to analyze the doping-driven metal-insulator transition in a (2+1)-dimensional Hubbard model, revealing the transition across various coupling strengths.

Contribution

It applies tensor renormalization group techniques to explore the metal-insulator transition in the Hubbard model at different Coulomb interactions, providing new insights into the phase behavior.

Findings

Identified critical chemical potentials for the transition at different U values.

Demonstrated the transition occurs over a wide range of finite couplings.

Confirmed the presence of a metal-insulator transition across various interaction strengths.

Abstract

We investigate the doping-driven metal-insulator transition of the (2+1)-dimensional Hubbard model in the path-integral formalism with the tensor renormalization group method. We calculate the electron density $\langle n\rangle$ as a function of the chemical potential $\mu$ choosing three values of the Coulomb potential with $U=80$, $8$, and $2$ as representative cases of the strong, intermediate, and weak couplings. We have determined the critical chemical potential at each $U$, where the Hubbard model undergoes the metal-insulator transition from the half-filling plateau with $\langle n\rangle=1$ to the metallic state with $\langle n\rangle > 1$. Our results indicate that the model exhibits the metal-insulator transition over the vast region of the finite coupling $U$.