{"ID":2898766,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.02644","arxiv_id":"2507.02644","title":"Solving the Hubbard model with Neural Quantum States","abstract":"The rapid development of neural quantum states (NQS) has established it as a promising framework for studying quantum many-body systems. In this work, by leveraging the cutting-edge transformer-based architectures and developing highly efficient optimization algorithms, we achieve the state-of-the-art results for the doped two-dimensional (2D) Hubbard model, arguably the minimum model for high-Tc superconductivity. Interestingly, we find different attention heads in the NQS ansatz can directly encode correlations at different scales, making it capable of capturing long-range correlations and entanglements in strongly correlated systems. With these advances, we establish the half-filled stripe in the ground state of 2D Hubbard model with the next nearest neighboring hoppings, consistent with experimental observations in cuprates. Our work establishes NQS as a powerful tool for solving challenging many-fermions systems.","short_abstract":"The rapid development of neural quantum states (NQS) has established it as a promising framework for studying quantum many-body systems. In this work, by leveraging the cutting-edge transformer-based architectures and developing highly efficient optimization algorithms, we achieve the state-of-the-art results for the d...","url_abs":"https://arxiv.org/abs/2507.02644","url_pdf":"https://arxiv.org/pdf/2507.02644v2","authors":"[\"Yuntian Gu\",\"Wenrui Li\",\"Heng Lin\",\"Bo Zhan\",\"Ruichen Li\",\"Yifei Huang\",\"Di He\",\"Yantao Wu\",\"Tao Xiang\",\"Mingpu Qin\",\"Liwei Wang\",\"Dingshun Lv\"]","published":"2025-07-03T14:08:25Z","proceeding":"cond-mat.str-el","tasks":"[\"cond-mat.str-el\",\"cs.AI\",\"quant-ph\"]","methods":"[\"Transformer\"]","has_code":false}