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arXiv · 2006.00300

Low-complexity eigenstates of a $\nu = 1/3$ fractional quantum Hall system

Bruno Nachtergaele·Simone Warzel·Amanda Young
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Abstract

We identify the the ground-state of a truncated version of Haldane's pseudo-potential Hamiltonian in a thin cylinder geometry as being composed of exponentially many fragmented matrix product states. These states are constructed by lattice tilings and their properties are discussed. We also report on a proof of a spectral gap, which implies the incompressibility of the underlying fractional quantum Hall liquid at maximal filling $\nu = 1/3$. Low-energy excitations and an extensive number of many-body scars at positive energy density, but nevertheless low complexity, are also identified using the concept of tilings.

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Bruno Nachtergaele, Simone Warzel, Amanda Young. 2020-05-30. Low-complexity eigenstates of a $\nu = 1/3$ fractional quantum Hall system. https://doi.org/10.1088/1751-8121%2Fabca73

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