TY - JOUR

T1 - Entanglement gap and a new principle of adiabatic continuity

AU - Thomale, R.

AU - Sterdyniak, A.

AU - Regnault, N.

AU - Bernevig, B. Andrei

N1 - Copyright:
Copyright 2010 Elsevier B.V., All rights reserved.

PY - 2010/5/3

Y1 - 2010/5/3

N2 - 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.

AB - 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.

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U2 - 10.1103/PhysRevLett.104.180502

DO - 10.1103/PhysRevLett.104.180502

M3 - Article

C2 - 20482158

AN - SCOPUS:77951931788

VL - 104

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 18

M1 - 180502

ER -