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<p>Neural networks have shown to be a powerful tool to represent the ground state of quantum many-body systems, including fermionic systems. However, efficiently integrating lattice symmetries into neural representations remains a significant challenge. In this work, we introduce a framework for embedding lattice symmetries in fermionic wavefunctions and demonstrate its ability to target both ground states and low-lying excitations. Using group-equivariant neural backflow transformations, we study the <i>t</i>-<i>V</i> model on a square lattice away from half-filling. Our symmetry-aware backflow significantly improves ground-state energies and yields accurate low-energy excitations for lattices up to 10&#xa0;×&#xa0;10. We also compute accurate two-point density-correlation functions and the structure factor to identify phase transitions and critical points. These findings introduce a symmetry-aware framework important for studying quantum materials and phase transitions.</p>

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Spectroscopy of two-dimensional interacting lattice electrons using symmetry-aware neural backflow transformations

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年1月30日

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  • Imelda Romero,
  • Jannes Nys,
  • Giuseppe Carleo

摘要

Neural networks have shown to be a powerful tool to represent the ground state of quantum many-body systems, including fermionic systems. However, efficiently integrating lattice symmetries into neural representations remains a significant challenge. In this work, we introduce a framework for embedding lattice symmetries in fermionic wavefunctions and demonstrate its ability to target both ground states and low-lying excitations. Using group-equivariant neural backflow transformations, we study the t-V model on a square lattice away from half-filling. Our symmetry-aware backflow significantly improves ground-state energies and yields accurate low-energy excitations for lattices up to 10 × 10. We also compute accurate two-point density-correlation functions and the structure factor to identify phase transitions and critical points. These findings introduce a symmetry-aware framework important for studying quantum materials and phase transitions.