Romero Imelda, Nys Jannes, Carleo Giuseppe
Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland.
Center for Quantum Science and Engineering, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland.
Commun Phys. 2025;8(1):46. doi: 10.1038/s42005-025-01955-z. Epub 2025 Jan 30.
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 - 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.
神经网络已被证明是表示量子多体系统基态的有力工具，包括费米子系统。然而，有效地将晶格对称性整合到神经表示中仍然是一个重大挑战。在这项工作中，我们引入了一个在费米子波函数中嵌入晶格对称性的框架，并展示了其针对基态和低激发态的能力。使用群等变神经回流变换，我们研究了远离半填充的方形晶格上的-模型。我们的对称性感知回流显著提高了基态能量，并为高达10×10的晶格产生了准确的低能激发。我们还计算了准确的两点密度关联函数和结构因子，以识别相变和临界点。这些发现引入了一个对研究量子材料和相变很重要的对称性感知框架。
