An Exactly Solvable Model for Strongly Interacting Electrons in a Magnetic Field

Abstract

States of strongly interacting particles are 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 short-range 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.

References in corpus (13)

• Non-Abelian Anyons and Topological Quantum Computation
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Geometrical Description of the Fractional Quantum Hall Effect
• Topological Entanglement and Clustering of Jain Hierarchy States
• A nu=2/5 Paired Wavefunction
• Model anisotropic quantum Hall states
• Non-Abelian Parton Fractional Quantum Hall Effect in Multilayer Graphene
• Composite Fermions on a Torus
• Entangled Pauli Principles: the DNA of Quantum Hall Fluids
• Entanglement Spectrum of Composite Fermion States in Real Space
• Local two-body parent Hamiltonians for the entire Jain sequence
• Composite Fermion states on the torus

Cited by in corpus (6)

• The composite fermion theory revisited: a microscopic derivation without Landau level projection
• Real-space entanglement spectra of projected fractional quantum Hall states using Monte Carlo methods
• Exactly Solvable Hamiltonian for Non-Abelian Quasiparticles
• Torus geometry eigenfunctions of an interacting multi-Landau level Hamiltonian
• Non-Abelian topological order with SO(5)${}_1$ chiral edge states
• Candidate local parent Hamiltonian for 3/7 fractional quantum Hall effect