Grassmann corner transfer-matrix renormalization group approach to one-dimensional fermionic models
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| Format: | Preprint |
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2026
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| _version_ | 1866908942176616448 |
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| author | Kong, Jian-Gang Xie, Zhi Yuan |
| author_facet | Kong, Jian-Gang Xie, Zhi Yuan |
| contents | The strongly correlated fermions play a vital role in modern physics. For a given fermionic Hamiltonian system, the most widely used approach to explore the underlying physics is to study the wave function that incorporates Fermi-Dirac statistics, which can be obtained variationally by energy minimization or by imaginary-time evolution. In this work, we develop an accurate tensor network method for one-dimensional interacting fermionic models based on the coherent-state path-integral representation of the fermionic partition function. Employing the coherent-state representation, the partition function is effectively represented as a (1+1)-dimensional anisotropic Grassmann-valued tensor network, and the Grassmann version of the corner transfer-matrix renormalization group algorithm is developed to contract the tensor network and evaluate physical quantities. We validate our method in the one-dimensional fermionic Hubbard model with a magnetic field, where the essential features of the phase diagram in the $(μ, B)$ plane are quantitatively captured. Our work offers a promising approach to interacting fermionic models within the framework of tensor networks. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_05582 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Grassmann corner transfer-matrix renormalization group approach to one-dimensional fermionic models Kong, Jian-Gang Xie, Zhi Yuan Strongly Correlated Electrons The strongly correlated fermions play a vital role in modern physics. For a given fermionic Hamiltonian system, the most widely used approach to explore the underlying physics is to study the wave function that incorporates Fermi-Dirac statistics, which can be obtained variationally by energy minimization or by imaginary-time evolution. In this work, we develop an accurate tensor network method for one-dimensional interacting fermionic models based on the coherent-state path-integral representation of the fermionic partition function. Employing the coherent-state representation, the partition function is effectively represented as a (1+1)-dimensional anisotropic Grassmann-valued tensor network, and the Grassmann version of the corner transfer-matrix renormalization group algorithm is developed to contract the tensor network and evaluate physical quantities. We validate our method in the one-dimensional fermionic Hubbard model with a magnetic field, where the essential features of the phase diagram in the $(μ, B)$ plane are quantitatively captured. Our work offers a promising approach to interacting fermionic models within the framework of tensor networks. |
| title | Grassmann corner transfer-matrix renormalization group approach to one-dimensional fermionic models |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2604.05582 |