Tensor renormalization group approach to (1+1)-dimensional Hubbard model

TL;DR

This paper applies the tensor renormalization group method to analyze the (1+1)-dimensional Hubbard model, successfully determining critical parameters and demonstrating the method's potential for studying higher-dimensional models.

Contribution

It introduces a tensor renormalization group approach to the Hubbard model, providing accurate critical parameters and validating its effectiveness against exact solutions.

Findings

Accurately determined critical chemical potential and exponent.

Results consistent with Bethe ansatz solutions.

Showed potential for extending to higher-dimensional models.

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