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arXiv · 2604.05582

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

Jian-Gang Kong·Zhi-Yuan Xie
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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 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 $(\mu, B)$ plane are quantitatively captured. Our work offers a promising approach to interacting fermionic models within the framework of tensor networks.

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Jian-Gang Kong, Zhi-Yuan Xie. 2026-04-07. Grassmann corner transfer-matrix renormalization group approach to one-dimensional fermionic models. https://doi.org/10.1088/1674-1056%2Fae56e3

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