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Fractional Hall Physics from Large N Interacting Fermions

Kristan Jensen1,* and Amir Raz2,†

  • *Contact author: kristanj@uvic.ca
  • †Contact author: araz@utexas.edu
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Phys. Rev. Lett. 135, 071601 – Published 14 August, 2025

DOI: https://doi.org/10.1103/bn5v-p282

Abstract

We solve models of N species of fermions in the lowest Landau level with U(N)-invariant interactions in the N≫1 limit. We find saddles of the second quantized path integral at fixed chemical potential corresponding to fractional Hall states with filling (p/q), where the integers p and q depend on the chemical potential and interactions. On a long torus there are q such states related by translation symmetry, and SU(N)-invariant excitations of fractional charge. Remarkably, these saddles and their filling persist as extrema of the second-quantized action at N=1. Our construction gives a first-principles derivation of fractional Hall states from strongly interacting fermions.

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Phys. Rev. Lett. 135, 071601– Published 14 August, 2025
  • Received 8 February 2024
  • Revised 7 February 2025
  • Accepted 18 July 2025
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