arXiv subjects

Jian-Gang Kong

Publications and source records attributed to Jian-Gang Kong.

5 recordsLinked to original sources

arXiv2026

Grassmann tensor networks

Developing non-perturbative methods to reveal exotic properties of strongly correlated fermionic systems remains one of the most essential tasks of theoretical physics. Tensor network methods with Grassmann algebra offer powerful numerical tools for fermionic many-body systems in the coherent-state path-integral representation. Despite their vast potential for both condensed-matter and particle-physics communities, Grassmann tensor network methods are somewhat underexploited in practical simulations. In this work, we provide a detailed, self-contained introduction to Grassmann tensor network methods, from the basics of the Grassmann tensor operations to the Grassmannization of typical tensor network algorithms. Furthermore, the resulting Grassmann tensor network methods are validated in several interesting models in both particle physics and condensed matter physics.

cond-mat.str-el↗

arXiv2026

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

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.

cond-mat.str-el↗

arXiv2026

Phase diagram of the single-flavor Gross--Neveu--Wilson model from the Grassmann corner transfer matrix renormalization group

We investigate the phase structure of the single-flavor Gross--Neveu model with Wilson fermions using the Grassmann corner transfer matrix renormalization group (CTMRG). The path integral is formulated as a two-dimensional Grassmann tensor network and approximately contracted by the Grassmann CTMRG algorithm. We investigate the phase diagram by varying the fermion mass and the four-fermion coupling, using the pseudoscalar condensate as an order parameter for the $\mathbb{Z}_{2}$ parity symmetry breaking phase. The universality classes of the phase boundaries are identified through the central charge $c$ obtained via scaling analysis of the entanglement entropy. Furthermore, we extract the quantity related to the entanglement spectrum from the converged CTMRG environments, allowing us to distinguish the topological insulator phase and the trivial phase. The resulting phase structure suggests that the Aoki phase is separated from the other phases by critical lines characterized by $c=1/2$, while the critical lines with $c=1$ separate the topological insulating and trivial phases. Our numerical results also indicate that the Aoki phase does not persist in the strong-coupling regime for the single-flavor theory.

hep-lat↗

arXiv2024

Self-supervised Representations and Node Embedding Graph Neural Networks for Accurate and Multi-scale Analysis of Materials

Supervised machine learning algorithms, such as graph neural networks (GNN), have successfully predicted material properties. However, the superior performance of GNN usually relies on end-to-end learning on large material datasets, which may lose the physical insight of multi-scale information about materials. And the process of labeling data consumes many resources and inevitably introduces errors, which constrains the accuracy of prediction. We propose to train the GNN model by self-supervised learning on the node and edge information of the crystal graph. Compared with the popular manually constructed material descriptors, the self-supervised atomic representation can reach better prediction performance on material properties. Furthermore, it may provide physical insights by tuning the range information. Applying the self-supervised atomic representation on the magnetic moment datasets, we show how they can extract rules and information from the magnetic materials. To incorporate rich physical information into the GNN model, we develop the node embedding graph neural networks (NEGNN) framework and show significant improvements in the prediction performance. The self-supervised material representation and the NEGNN framework may investigate in-depth information from materials and can be applied to small datasets with increased prediction accuracy.

cond-mat.mtrl-sci↗

arXiv2022

Self-supervised graph neural networks for accurate prediction of Néel temperature

Antiferromagnetic materials are exciting quantum materials with rich physics and great potential for applications. It is highly demanded of the accurate and efficient theoretical method for determining the critical transition temperatures, Néel temperatures, of antiferromagnetic materials. The powerful graph neural networks (GNN) that succeed in predicting material properties lose their advantage in predicting magnetic properties due to the small dataset of magnetic materials, while conventional machine learning models heavily depend on the quality of material descriptors. We propose a new strategy to extract high-level material representations by utilizing self-supervised training of GNN on large-scale unlabeled datasets. According to the dimensional reduction analysis, we find that the learned knowledge about elements and magnetism transfers to the generated atomic vector representations. Compared with popular manually constructed descriptors and crystal graph convolutional neural networks, self-supervised material representations can help us obtain a more accurate and efficient model for Néel temperatures, and the trained model can successfully predict high Néel temperature antiferromagnetic materials. Our self-supervised GNN may serve as a universal pre-training framework for various material properties.

cond-mat.mtrl-sci↗