Grassmann corner transfer-matrix renormalization group approach to one-dimensional fermionic models

doi:10.1088/1674-1056/ae56e3

中国物理B ›› 2026, Vol. 35 ›› Issue (6): 67101-067101.doi: 10.1088/1674-1056/ae56e3

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

收稿日期:2026-01-24 修回日期:2026-03-15 接受日期:2026-03-25 出版日期:2026-05-28 发布日期:2026-05-28
通讯作者: Zhi-Yuan Xie E-mail:qingtaoxie@ruc.edu.cn
基金资助:
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).

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

Received:2026-01-24 Revised:2026-03-15 Accepted:2026-03-25 Online:2026-05-28 Published:2026-05-28
Contact: Zhi-Yuan Xie E-mail:qingtaoxie@ruc.edu.cn
Supported by:
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).

1. 2026-067101-SI.pdf(72KB)

摘要/Abstract

摘要： 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.

关键词: Grassmann tensor network, fermionic path integral, partition function

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.

Key words: Grassmann tensor network, fermionic path integral, partition function

中图分类号: (Lattice fermion models (Hubbard model, etc.))

71.10.Fd

05.10.Cc (Renormalization group methods)

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[J]. 中国物理B, 2026, 35(6): 67101-067101.

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[J]. Chin. Phys. B, 2026, 35(6): 67101-067101.

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Grassmann corner transfer-matrix renormalization group approach to one-dimensional fermionic models

Grassmann corner transfer-matrix renormalization group approach to one-dimensional fermionic models

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