Exactly solvable fermion chain describing a $ν=1/3$ fractional quantum Hall state

Details Exactly solvable fermion chain describing a $ν=1/3$ fractional quantum Hall state Exactly solvable fermion chain describing a $ν=1/3$ fractional quantum Hall state

2011-10-23

arxiv.org/abs/1110.5033v2

Physics

Condensed Matter

Strongly Correlated Electrons

4 pages. 3 figures

Scientific paper

We introduce an exactly solvable fermion chain which describes a $\nu=1/3$ 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 which 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.

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