Entanglement Gap and a New Principle of Adiabatic Continuity

We give a complete definition of the entanglement gap separating low-energy, topological levels from high-energy, generic ones, in the entanglement spectrum of fractional quantum Hall (FQH) states. This is accomplished by removing the magnetic length inherent in the FQH problem-a procedure which we call taking the conformal limit. The counting of the low-lying entanglement levels starts off as the counting of modes of the edge theory of the FQH state, but quickly develops finite-size effects which we find to serve as a fingerprint of the FQH state. As the sphere manifold where the FQH resides grows, the level spacing of the states at the same angular momentum goes to zero, suggestive of the presence of relativistic gapless edge states. By using the adiabatic continuity of the low-entanglement energy levels, we investigate whether two states are topologically connected.