An exactly solvable model of strongly interacting fermions in a magnetic field

The lowest Landau level fractional quantum Hall (LLL-FQH) states are well understood as integer quantum Hall (IQH) states of weakly interacting composite fermions occupying Landau levels in an effective magnetic field. Their wavefunctions closely approximate the Coulomb eigenstates but in general are not exact eigenstates of any known local Hamiltonians [1]. We present a model Hamiltonian for strongly interacting spin-polarized fermions of filling fractions less than 1/2 in the limit where the interaction is strong compared to the cyclotron energy [2].  The Hamiltonian produces the same low energy quantum numbers as the composite fermions wavefunctions describing LLL-FQH states while allowing exact formal solutions to ground states, quasihole, quasiparticle and neutral excitations at arbitrary filling fractions of the form n/(2pn+1). We present results in the spherical, torus and cylindrical geometries to demonstrate the one-to-one correspondence with the non interacting fermion model in an effective magnetic field. We also show numerical results from exact diagonalization, Monte Carlo and iDMRG studies testing the adiabatic connection with Coulomb physics, quasiparticle Berry phase and charge [3].

This work was supported by funds from the U.S. Department of Energy, Office of Science, Basic Energy Sciences, under Award No. DE-SC0005042 and  Government of India, DST SERB Grant No. ECR/2018/001781