Spectral Gaps and Incompressibility in a $ \nu = 1/3 $ Fractional Quantum Hall System

Understand

We study an effective Hamiltonian for the standard $\nu=1/3$ fractional quantum Hall system in the thin cylinder regime.

• We give a complete description of its ground state space in terms of what we call Fragmented Matrix Product States, which are labeled by a certain family of tilings of the one-dimensional lattice.
• We then prove that the model has a spectral gap above the ground states for a range of coupling constants that includes physical values.
• As a consequence of the gap we establish the incompressibility of the fractional quantum Hall states.