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

TL;DR

This paper introduces a symmetry-aware neural network framework for accurately modeling the ground state and excitations of two-dimensional lattice fermion systems, improving energy estimates and phase transition detection.

Contribution

The work develops a group-equivariant neural backflow method that effectively incorporates lattice symmetries into fermionic wavefunctions, enhancing simulation accuracy.

Findings

Improved ground-state energy estimates for the t-V model.

Accurate low-energy excitation calculations on 10x10 lattices.

Identification of phase transitions via structure factor analysis.

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.