Microscopic study of the 2/5 fractional quantum Hall edge

Abstract

This paper reports on our study of the edge of the 2/5 fractional quantum Hall state, which is more complicated than the edge of the 1/3 state because of the presence of a continuum of quasi-degenerate edge sectors corresponding to different partitions of composite fermions in the lowest two Λ levels. The addition of an electron at the edge is a non-perturbative process and it is not a priori obvious in what manner the added electron distributes itself over these sectors. We show, from a microscopic calculation, that when an electron is added at the edge of the ground state in the [N_1, N_2] sector, where N_1 and N_2 are the numbers of composite fermions in the lowest two Λ levels, the resulting state lies in either [N_1 + 1, N_2] or [N_1, N_2 + 1] sector; adding an electron at the edge is thus equivalent to adding a composite fermion at the edge. The coupling to other sectors of the form [N_1 + 1 + k, N_2 - k], k integer, is negligible in the asymptotically low-energy limit. This study also allows a detailed and substantial comparison with the two-boson model of the 2/5 edge. We compute the spectral weights and find that while the individual spectral weights are complicated and non-universal, their sum is consistent with an effective two-boson description of the 2/5 edge.

11 pages, 7 figures

References in corpus (6)

• Composite fermion wave functions as conformal field theory correlators
• Quantum Hall quasielectron operators in conformal field theory
• Testing the topological nature of the fractional quantum Hall edge
• Fractional quantum Hall edge: Effect of nonlinear dispersion and edge roton
• Semiconductor quantum dots in high magnetic fields: The composite-fermion view
• Correlated tunneling and the instability of the fractional quantum Hall edge

Cited by in corpus (9)

• Quantum Hall Effect of Two-Component Bosons at Fractional and Integral Fillings
• Entanglement Spectrum of Composite Fermion States in Real Space
• Microscopic Study of Edge Excitations of Spin-Polarized and Spin-Unpolarized $\nu =2/3$ Fractional Quantum Hall Effect
• Real-space entanglement spectra of parton states in fractional quantum Hall systems
• Chiral Luttinger liquids and a generalized Luttinger's theorem in fractional quantum Hall edges via finite-entanglement scaling
• Composite fermion model for entanglement spectrum of fractional quantum Hall states
• Edge properties of principal fractional quantum Hall states in the cylinder geometry
• Many-body study of a quantum point contact in the fractional quantum Hall regime at v=5/2
• Edge reconstruction of compressible Quantum Hall fluid in the filling fraction range 1/3 to 2/3