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Solid State Communications

Analytically solvable microscopic model of fractional quantum Hall states

Neil F. Johnson, Luis Quiroga

Published Feb 1, 1994• 5 citations
Publisher
DOI
10.1016/0038-1098(94)90571-1

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We describe solvable models that capture how impurity scattering in certain fractional quantum Hall edges can give rise to a neutral mode---i.e., an edge mode that does not carry electric charge. These models consist of two counterpropagating chiral Luttinger liquids together with a collection of discrete impurity scatterers. Our main result is an exact solution of these models in the limit of infinitely strong impurity scattering. From this solution, we explicitly derive the existence of a neutral mode and we determine all of its microscopic properties including its velocity. We also study the stability of the neutral mode and show that it survives at finite but sufficiently strong scattering. Our results are applicable to a family of Abelian fractional quantum Hall states of which the $\ensuremath{\nu}=2/3$ state is the most prominent example.
We introduce an exactly solvable fermion chain that describes a ν=1/3 fractional quantum Hall (FQH) state beyond the thin-torus limit. The ground state of our model is shown to be unique for each center-of-mass sector, and it has a matrix product representation that enables us to exactly calculate order parameters, correlation functions, and entanglement spectra. The ground state of our model shows striking similarities with the BCS wave functions and quantum spin-1 chains. Using the variational method with matrix product ansatz, we analytically calculate excitation gaps and vanishing of the compressibility expected in the FQH state. We also show that the above results can be related to a ν=1/2 bosonic FQH state.