Exactly Solvable Model for Strongly Interacting Electrons in a Magnetic Field

States of strongly interacting particles arc of fundamental interest in physics and can produce exotic emergent phenomena and topological structures. We consider here two-dimensional electrons in a magnetic field, and, departing from the standard practice of restricting to the lowest LL, introduce a model shortrange interaction that is infinitely strong compared to the cyclotron energy. We demonstrate that this model lends itself to an exact solution for the ground as well as excited states at arbitrary filling factors nu < 1/2p and produces a fractional quantum Hall effect at fractions of the form nu = n/(2pn + 1), where n and p are integers. The fractional quantum Hall states of our model share many topological properties with the corresponding Coulomb ground states in the lowest Landau level, such as the edge physics and the fractional charge of the excitations.

Automated summary

The study examines the states of strongly interacting particles, focusing on two-dimensional electrons in a magnetic field with a model short-range interaction. The model reveals a fractional quantum Hall effect and shares many topological properties with the Coulomb ground states, showing similar edge physics and fractional charge of excitations.