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The edge physics of the $\nu=5/2$ fractional quantum Hall state is ofrelevance to several recent experiments that use it as a probe to gain insightinto the nature of the bulk state. We perform calculations in a semi-realisticsetup with positive background charge at a distance $d$, by exactdiagonalization both in the full Hilbert space (neglecting Landau level mixing)and in the restricted Pfaffian basis of edge excitations. Our principal findingis that the 5/2 edge is unstable to a reconstruction except for very small $d$.In addition, the interactions between the electrons in the second Landau leveland the lowest Landau level enhance the tendency toward edge reconstruction. Weidentify the bosonic and fermionic modes of edge excitations and obtain theirdispersions by back-calculating from the energy spectra as well as directlyfrom appropriate trial wave functions. We find that the edge reconstruction isdriven by an instability in the fermionic sector for setback distances close tothe critical ones. We also study the edge of the $\nu=7/3$ state and find thatedge reconstruction occurs here more readily than for the $\nu=1/3$ state. Ourstudy indicates that the $\nu=5/2$ and 7/3 edge states are reconstructed forall experimental systems investigated so far and thus must be taken intoaccount when analyzing experimental results. We also consider an effectivefield theory to gain insight into how edge reconstruction might influencevarious observable quantities.

Theoretical investigation of edge reconstruction in the $\nu$=5/2 and 7/3 fractional quantum Hall states