论文标题
$ν= 1/3 $分数量子厅系统的光谱差距和不可压缩性
Spectral Gaps and Incompressibility in a $ ν= 1/3 $ Fractional Quantum Hall System
论文作者
论文摘要
我们研究了薄缸制度中标准$ν= 1/3 $分数量子厅系统的有效哈密顿量。我们从所谓的零碎矩阵产品状态来完整地描述了其基态空间，这些状态被一维晶格的某个瓷砖家族标记。然后，我们证明该模型在包含物理值的一系列耦合常数方面具有高于接地状态的光谱差距。由于差距，我们建立了分数量子厅态的不可压缩性。我们还表明，所有用平铺标记的基态都具有有限的相关长度，我们给出了上限。但是，我们以举例说明，并非所有平铺状态的叠加都具有相关性的指数衰减。
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.
