Tensor renormalization group approach to (1+1)-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 ${\mu }_{\mathrm{c}}$ 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.

arXiv comment15 pages, 7 figures

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• Tensor renormalization group study of (1+1)-dimensional U(1) gauge-Higgs model at $\theta =\pi$ with Lüscher's admissibility condition
• Quantum Field Theories with Tensor Renormalization Group
• Spectroscopy with the tensor renormalization group method
• Triad representation for the anisotropic tensor renormalization group in four dimensions
• Forward-mode automatic differentiation for the tensor renormalization group and its relation to the impurity method
• Metal-insulator transition in (2+1)-dimensional Hubbard model with tensor renormalization group
• Tensor renormalization group study of cold and dense QCD in the strong coupling limit
• Phase diagram of the single-flavor Gross--Neveu--Wilson model from the Grassmann corner transfer matrix renormalization group
• Grassmann tensor networks