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

Area of Science:

• Quantum physics
• Computational condensed matter physics
• Machine learning in physics

Background:

• Neural networks are effective for representing quantum many-body ground states.
• Integrating lattice symmetries into neural representations of fermionic systems is challenging.

Purpose of the Study:

• Introduce a framework for embedding lattice symmetries in fermionic wavefunctions.
• Demonstrate its capability to target ground states and low-lying excitations.
• Apply the framework to the t-V model on a square lattice.

Main Methods:

• Utilized group-equivariant neural backflow transformations.
• Embedded lattice symmetries into neural network architectures.
• Studied the t-V model away from half-filling on square lattices up to 10x10.

Main Results:

• Achieved significant improvements in ground-state energies.
• Obtained accurate low-energy excitations.
• Computed accurate two-point density-correlation functions and structure factor.
• Identified phase transitions and critical points.

Conclusions:

• The developed symmetry-aware framework is crucial for studying quantum materials.
• This approach enhances the accuracy of neural network representations for quantum systems.
• It provides a powerful tool for investigating quantum phase transitions.