Entanglement Spectral Flows of Fractional Quantum Hall states

Abstract

The ground state entanglement spectra of topological phases are related to the spectra of their physical edge modes and can therefore be used to identify and characterize their topological order. In this thesis, we numerically study entanglement spectral flows of the model fractional quantum Hall ground states, namely the v = 1/3 Laughlin state and v = 5/2 Moore-Read state, on the cylinder. We introduce the ‘orbital spectral flow’, an interpolation scheme between orbitals that generalizes the orbital entanglement spectrum, and ‘real space spectral flow’, a flow that adiabatically connects the particle entanglement spectrum to the orbital entanglement spectrum. Using the orbital spectral flow, we find that the root configuration of the model states can be identified by looking at the lowest lying part of the flow. By looking at the ‘mismatches’ of the orbital spectral flow for the v = 5/2 Moore-Read state, we are able to identify that there are two sectors of the associated conformal field theory with different level countings. Using the real space spectral flow, we see that the levels of the orbital entanglement spectrum are in general lower than the levels associated with the real space entanglement spectrum throughout the flow, indicating that the low energy physics is always dominated by the conformal field theory which is associated with the interacting part of the fractional quantum Hall state.