Neural Network-Based Variational Wavefunctions for the Fractional Quantum Hall Effect

The fractional quantum Hall effect (FQHE) is a paradigmatic example of a strongly correlated quantum system in which electron-electron interactions give rise to exotic topological phases. Accurately simulating such systems requires the development of advanced many-electron wave function approximation methods. In this work, we explore a neural network-based variational Monte Carlo approach for approximating ground state wavefunctions in FQHE systems.

We compute ground-state energies in lowest-Landau-level projected Hilbert spaces for various FQHE filling fractions, comparing the results with Laughlin wavefunctions and exact diagonalization. Our findings indicate that neural networks can enhance the expressiveness of variational wavefunctions, yielding accurate energy estimates and correlation functions. This study highlights the potential of neural network architectures to expand the scope of variational quantum simulations, paving the way for new insights into topological quantum systems and quantum many-body physics.