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

Fuente: arXiv
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Main Authors: Kong, Jian-Gang, Xie, Zhi Yuan
Format: Preprint
Published: 2026
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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
id 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