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

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 $⟨n⟩$ 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 $⟨n⟩=1$ to the metallic state with $⟨n⟩>1$. Our results indicate that the model exhibits the metal-insulator transition over the vast region of the finite coupling $U$.

Comments: 6 pages, 7 figures