Microscopic realization of fractional Hall conductance

Construct a microscopic model for which the ground state has rigorously provable fractional Hall conductance.

Background

The authors describe the absence of a known microscopic example proving fractional Hall conductance as a central puzzle in the theory of the fractional quantum Hall effect.

They contrast this gap with the existence of exactly solvable models realizing modular tensor categories associated with quantum doubles. The unresolved task is to produce a concrete microscopic Hamiltonian whose ground state is known mathematically to exhibit fractional Hall conductance.