Abstract

In recent years, with the accelerated development of artificial intelligence, a growing field of computational quantum chemistry is the use of neural networks as ansatze for variational Monte Carlo calculations. This neural wave functions approach has been demonstrated to be a very accurate technique for obtaining numerical solutions of the Schrodinger equation. I will start by giving an introduction to the field of neural-network variational Monte Carlo, followed by how we have recently adapted them to study the fractional quantum Hall effect.

The fractional quantum Hall effect hosts emergent anyons with exotic exchange statistics, but direct numerical access to their topological properties in the continuum has remained limited. Most computational approaches are restricted to a single Landau level, which precludes treating realistic regimes with strong Landau-level mixing. Using neural-network variational Monte Carlo, we obtain the 3 degenerate ground states at filling factor ν = 1/3. From these states, we extract the modular S matrix via entanglement interferometry, a technique previously applied only to lattice models. The resulting S matrix encodes the quantum dimensions, fusion rules, and exchange statistics of the emergent anyons, providing a direct numerical demonstration of their topological order. The calculated anyon properties match the well-known theoretical and experimental results. Our work establishes neural-network wavefunctions as a powerful new tool for investigating anyonic properties.