We investigate the metal-insulator transition of the ($1+1$)-dimensional Hubbard model in the path-integral formalism with the tensor renormalization group method. The critical chemical potential ${\mu }_{\mathrm{c}}$ and the critical exponent $\nu$ are determined from the $\mu$ dependence of the electron density in the thermodynamic limit. Our results for ${\mu }_{\mathrm{c}}$ and $\nu$ show consistency with an exact solution based on the Bethe ansatz. Our encouraging results indicate the applicability of the tensor renormalization group method to the analysis of higher-dimensional Hubbard models.

• Received 14 May 2021
• Accepted 10 June 2021

DOI:https://doi.org/10.1103/PhysRevD.104.014504

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Published by the American Physical Society