$ ν= 1/3 $分数量子Hall系统的谱隙和不可压缩性
Spectral Gaps and Incompressibility in a $ ν= 1/3 $ Fractional Quantum Hall System
摘要：
研究了薄圆柱体系中标准$ν=1/3$分数量子Hall系统的有效哈密顿量.我们给出了一个完整的描述，它的基态空间中，我们称之为碎片矩阵产品的国家，这是由一定的家庭的平铺的一维晶格标记。然后，我们证明了该模型有一个光谱间隙以上的基态的耦合常数，其中包括物理值的范围。作为带隙的结果，我们建立了分数量子霍尔态的不可压缩性。我们还表明，所有的基态标记的平铺有一个有限的相关长度，我们给了一个上限。然而，我们通过例子证明，并不是所有的叠加平铺状态的相关性指数衰减。
英文摘要：
We study an effective Hamiltonian for the standard $ν=1/3$ 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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