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 $\nu =5/2$.

arXiv comment7 pages, 8 figures

References in corpus (24)

• Topological entanglement entropy
• Detecting topological order in a ground state wave function
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
• Sharp and Smooth Boundaries of Quantum Hall Liquids
• Geometrical Description of the Fractional Quantum Hall Effect
• Fractional Quantum Hall States and Jack Polynomials
• Ground state entanglement and geometric entropy in the Kitaev's model
• The entanglement gap and a new principle of adiabatic continuity
• Reconstruction of Fractional Quantum Hall Edges
• Real-Space Entanglement Spectrum of Quantum Hall States
• 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 $\nu =\frac{k}{r}$
• Real-space entanglement spectrum of quantum Hall systems
• Edge reconstruction in the fractional quantum Hall regime
• Model anisotropic quantum Hall states
• Evolution of Landau Levels into Edge States at an Atomically Sharp Edge in Graphene
• Evaluation of ranks of real space and particle entanglement spectra for large systems
• Edge-mode velocities and thermal coherence of quantum Hall interferometers
• Testing the topological nature of the fractional quantum Hall edge
• Realizing Universal Edge Properties in Graphene Fractional Quantum Hall Liquids
• 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
• Identification of the Fractional quantum Hall edge modes by density oscillations

Cited by in corpus (2)

• Density matrix renormalization group study of the $\nu =1/3$ edge states in fractional quantum Hall systems
• Bulk-edge Correspondence in the Adiabatic Heuristic Principle