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

Abstract

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 μ, choosing three values of the Coulomb potential with U = 80, 8, and 2 as representative cases of the strong, intermediate, and weak couplings. We determine 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 a vast region of the finite coupling U.