A self-attention fermionic neural network variationally solves the disk-geometry fractional quantum Hall problem including Landau level mixing, outperforming LLL-projected exact diagonalization and revealing short-distance wavefunction structure.
Electron bubbles in highly excited states of the lowest Landau level
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abstract
We study the entire energy spectrum of an electron droplet in the lowest Landau level. By exact diagonalization calculations, we find highly excited states in the middle of the spectrum that display unexpected density distribution and pair correlation. We show that these exceptional excited states contain tightly bound electron bubbles with local filling $\nu = 1$ that form various ordered structures. Remarkably, these bubble excited states are shown to exist for both the $1/r$ Coulomb interaction and the $1/r^3$ dipole interaction. The experimental realization of bubble excited states in moir\'e materials under a magnetic field is also discussed.
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Solving and visualizing fractional quantum Hall wavefunctions with neural network
A self-attention fermionic neural network variationally solves the disk-geometry fractional quantum Hall problem including Landau level mixing, outperforming LLL-projected exact diagonalization and revealing short-distance wavefunction structure.