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arXiv · 2004.04992

Spectral Gaps and Incompressibility in a $ \nu = 1/3 $ Fractional Quantum Hall System

Bruno Nachtergaele·Simone Warzel·Amanda Young
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Abstract

We study an effective Hamiltonian for the standard $\nu=1/3$ fractional quantum Hall system in the thin cylinder regime. We give a complete description of its ground state space in terms of what we call Fragmented Matrix Product States, which are labeled by a certain family of tilings of the one-dimensional lattice. We then prove that the model has a spectral gap above the ground states for a range of coupling constants that includes physical values. As a consequence of the gap we establish the incompressibility of the fractional quantum Hall states. We also show that all the ground states labeled by a tiling have a finite correlation length, for which we give an upper bound. We demonstrate by example, however, that not all superpositions of tiling states have exponential decay of correlations.

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Bruno Nachtergaele, Simone Warzel, Amanda Young. 2020-04-10. Spectral Gaps and Incompressibility in a $ \nu = 1/3 $ Fractional Quantum Hall System. https://doi.org/10.1007/s00220-021-03997-0

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