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Excited to share our latest preprint, on using deep learning to extract the weird fractional quantum statistics of 2D topological materials: arxiv.org/abs/2512.15872

Fundamental particles are either fermions or bosons. Fermions, like electrons, make up matter, while bosons, like photons, are force carriers. But in two dimensional materials in a magnetic field, things can start to get weird...

The collective excitations of many electrons behave a lot like particles...but instead of particles with integer spin (bosons) or half-integer spins (fermions) they behave like they have weird fractional spins like 1/3, 1/5, etc. This is the *fractional quantum hall effect*.

Rather than write down a solution through a stroke of genius, we trained a Transformer-like neural network to calculate these fractional spin statistics using "entanglement interferometry", and got answers more accurate than the Laughlin wavefunction.

This requires the calculation of multiple degenerate ground states. People have used neural networks to calculate *a* ground state for the FQHE, and have calculated fractional spin statistics in lattice models, but no one has done these calculations in the continuum before.

All-around fantastic work from Andres Perez Fadon and collaborators, and this shows how these calculations could be done for systems where we still don't know how to write down even qualitatively correct solutions.