We identify the ground-state of a truncated version of Haldane’s pseudo-potential Hamiltonian in the 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 ν = 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.

中文翻译：

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ν = 1/3分数量子霍尔系统的低复杂性本征态

我们将薄圆柱体几何中的Haldane伪势哈密顿量的截断形式的基态确定为由成指数分布的许多碎片矩阵乘积态组成。这些状态由晶格拼贴构成，并讨论了它们的性质。我们还报告了光谱间隙的证明，这表明最大填充ν = 1/3时基础分数量子霍尔液体的不可压缩性。使用平铺的概念还可以识别出低能量的激发和正能量密度下的大量多体疤痕，但是复杂度却很低。