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Abstract: We give a complete definition of the entanglement gap separating low-energy,topological levels, from high-energy, generic ones, in the -entanglementspectrum- of Fractional Quantum Hall FQH states. By removing the magneticlength inherent in the FQH problem - a procedure which we call taking the-conformal limit-, we find that the entanglement spectrum of an incompressibleground-state of a generic i.e. Coulomb lowest Landau Level Hamiltonianre-arranges into a low-entanglement energy part separated by a full gap fromthe high energy entanglement levels. As previously observed, the counting ofthese levels starts off as the counting of modes of the edge theory of the FQHstate, but quickly develops finite-size effects which we show can also serve asa fingerprint of the FQH state. As the sphere manifold where the FQH residesgrows, the level spacing of the states at the same angular momentum goes tozero, suggestive of the presence of relativistic gapless edge-states. By usingthe adiabatic continuity of the low entanglement energy levels, we investigatewhether two states are topologically connected.



Author: R. Thomale, A. Sterdyniak, N. Regnault, B. Andrei Bernevig

Source: https://arxiv.org/







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