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

• URL: http://arxiv.org/abs/2406.09077v2
• Date: Fri, 31 Jan 2025 08:49:56 GMT
• Title: Spectroscopy of two-dimensional interacting lattice electrons using symmetry-aware neural backflow transformations
• Authors: Imelda Romero, Jannes Nys, Giuseppe Carleo,
• Abstract summary: We introduce a framework for embedding lattice symmetries in fermionic wavefunctions and demonstrate its ability to target both ground states and low-lying excitations. Our symmetry-aware backflow significantly improves ground-state energies and yields accurate low-energy excitations for lattices up to 10 x 10.
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• Abstract: 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 x 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.

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