# Generalized Wigner crystal

On the Aharonov-Casher continuum model, neural quantum state variational Monte Carlo accommodates both fractional Chern insulators and generalized Wigner crystals and yields phase diagrams at fractional filling for up to 36 electrons with strong band mixing. Two wave functions, a flux-attachment form and a Slater-Jastrow form, describe topological order and crystalline order respectively, and their energies match multiband exact diagonalization on small systems. As the quantum geometry becomes more nonuniform, the Laughlin-like state at 1/3 filling keeps nearly constant energy while the Jain-like state at 2/5 filling drops, so the two respond differently to discrete translation symmetry.

On the Aharonov-Casher continuum model, neural quantum state variational Monte Carlo accommodates both fractional Chern insulators and generalized Wigner crystals and yields phase diagrams at fractional filling for up to 36 electrons with strong band mixing. Two wave functions, a flux-attachment form and a Slater-Jastrow form, describe topological order and crystalline order respectively, and their energies match multiband exact diagonalization on small systems. As the quantum geometry becomes more nonuniform, the Laughlin-like state at 1/3 filling keeps nearly constant energy while the Jain-like state at 2/5 filling drops, so the two respond differently to discrete translation symmetry.