Tensor renormalization group approach to (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math>)-dimensional Hubbard model

Abstract

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 ${\ensuremath{\mu}}_{\mathrm{c}}$ and the critical exponent $\ensuremath{\nu}$ are determined from the $\ensuremath{\mu}$ dependence of the electron density in the thermodynamic limit. Our results for ${\ensuremath{\mu}}_{\mathrm{c}}$ and $\ensuremath{\nu}$ 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.

Topics & Concepts