Spectrum of Quantum Entanglement in Fractional Quantum Hall States

Edward H. Rezayi, Jérôme Dubail, N. Read

Li-Xia Wei, Na Jiang, Qi Li +1 more

The edge of the electronic fractional quantum Hall (FQH) system obeys the law of the chiral Luttinger liquid theory due to its intrinsic topological properties and the relation of bulk-edge correspondence. However, in a realistic experimental system, such as the usual Hall bar setup, the softening of the background confinement potential can induce the reconstruction of the edge spectrum, which breaks the chirality and universality of the FQH edge. The entanglement spectrum (ES) of the FQH ground state has the same counting structure as that of the energy spectrum indicating the topological characters of the quantum state. In this work, we report that the ES can also have an edge reconstruction while sweeping the area of the subsystem in real space cut. Moreover, we found that the critical area of the subsystem matches accurately with the intrinsic building block of the FQH liquids, namely the correlation hole of the FQH liquids. The above results seem to be universal after our study of a series of typical FQH states, such as two Laughlin states at $\ensuremath{\nu}=1/3$ and $1/5$, and the Moore-Read state for $\ensuremath{\nu}=5/2$.

Antoine Sterdyniak

Simon C. Davenport, Ivan Dario Jimenez Rodriguez, Johannes K. Slingerland +1 more

We show that the entanglement spectrum associated with a certain class of strongly correlated many-body states---the wave functions proposed by Laughlin and Jain to describe the fractional quantum Hall effect---can be very well described in terms of a simple model of noninteracting (or weakly interacting) composite fermions.

Edward H. Rezayi

Ronny Thomale, Antoine Sterdyniak, Nicolas Regnault +1 more

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.