Entanglement spectrum edge reconstruction and correlation hole of the FQH liquids

Abstract

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 soften 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 in 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 sub-system in real space cut. Moreover, we found the critical area of the sub-system matches accurately with the intrinsic building block of the fractional quantum Hall liquids, namely the correlation hole of the FQH liquids. The above results seem like be universal after our studying a series of typical FQH states, such as two Laughlin states at $\nu =1/3$ and $\nu =1/5$, and the Moore-Read state for $\nu =5/2$.

7 pages, 8 figures

References in corpus (8)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Fractional Quantum Hall States and Jack Polynomials
• Ground state entanglement and geometric entropy in the Kitaev's model
• Fractional quantum Hall effect at $\nu =5/2$: Ground states, non-Abelian quasiholes, and edge modes in a microscopic model
• Properties of Non-Abelian Fractional Quantum Hall States at Filling $\nu =\frac{k}{r}$
• Testing the topological nature of the fractional quantum Hall edge
• Fractional quantum Hall edge: Effect of nonlinear dispersion and edge roton
• Theoretical investigation of edge reconstruction in the $\nu$=5/2 and 7/3 fractional quantum Hall states