Jack on a Devil's staircase

TL;DR

This paper reviews a mechanism for plateau formation in the fractional quantum Hall effect, linking microscopic Hamiltonians to a lattice gas model and explaining the Devil's staircase pattern through Jack polynomials.

Contribution

It introduces a mapping from the microscopic Hamiltonian to a lattice gas model, providing a new understanding of the ground states and their relation to Jack polynomials in the fractional quantum Hall effect.

Findings

Identification of a Devil's staircase pattern in quantum Hall plateaux

Connection between thin torus limit states and full system ground states

Exact eigenstates given by Jack polynomials

Abstract

We review a simple mechanism for the formation of plateaux in the fractional quantum Hall effect. It arises from a map of the microscopic Hamiltonian in the thin torus limit to a lattice gas model, solved by Hubbard. The map suggests a Devil's staircase pattern, and explains the observed asymmetries in the widths. Each plateau is a new ground state of the system: a periodic Slater state in the thin torus limit. We provide the unitary operator that maps such limit states to the full, effective ground states with same filling fraction. These Jack polynomials generalise Laughlin's ansatz, and are exact eigenstates of the Laplace-Beltrami operator. Why are Jacks sitting on the Devil's staircase? This is yet an intriguing problem.