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Grassmann corner transfer-matrix renormalization group approach to one-dimensional fermionic models |
| Jian-Gang Kong(孔建刚)1 and Zhi-Yuan Xie(谢志远)1,2,† |
1 School of Physics, Renmin University of China, Beijing 100872, China;
2 Key Laboratory of Quantum State Construction and Manipulation of MoE, Renmin University of China, Beijing 100872, China |
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Abstract The strongly correlated fermions play a vital role in modern physics. For a given fermionic Hamiltonian system, the most widely used approach to exploring 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 coherentstate 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 on 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.
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Received: 24 January 2026
Revised: 15 March 2026
Accepted manuscript online: 25 March 2026
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PACS:
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71.10.Fd
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(Lattice fermion models (Hubbard model, etc.))
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05.10.Cc
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(Renormalization group methods)
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| Fund: This work was supported by the National Natural Science Foundation of China (Grant No. 12274458) and the National Key R&D Program of China (Grant Nos. 2024YFA1408604 and 2023YFA1406500). |
Corresponding Authors:
Zhi-Yuan Xie
E-mail: qingtaoxie@ruc.edu.cn
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Cite this article:
Jian-Gang Kong(孔建刚) and Zhi-Yuan Xie(谢志远) Grassmann corner transfer-matrix renormalization group approach to one-dimensional fermionic models 2026 Chin. Phys. B 35 067101
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