论文标题
低填充处的分数量子厅液体与晶体相之间的相互作用
Interplay between fractional quantum Hall liquid and crystal phases at low filling
论文作者
论文摘要
在低兰道级填充因子下，国家的性质一直是分数量子大厅效应领域的一个长期难题。虽然理论计算表明，在填充因子$ν\ Lessim 1/6 $上受到青睐，但实验表明，在某种程度上升高的温度下，在纵向抵抗中的最小值与分数量子厅效应相关的$ν= $ν= $ν= $ 1/7、2/11、2/13、3/17、3/17、3/19、1/19、1/1/19、1/15和2/15 $ν= n/（6n \ pm 1）$和$ν= n/（8n \ pm 1）$。为了解决这个悖论，我们研究了一些低$ν$状态的性质，特别是$ν= 1/7 $，$ 2/13 $和$ 1/9 $，由变量蒙特卡洛，密度矩阵恢复量级化组和精确的对角色方法。我们得出的结论是，在热力学极限中，这些可能是不可压缩的分数量子霍尔液体，尽管具有很强的短距离晶体相关性。这表明了对实验观察到的行为的自然解释，并且是一个丰富的相图，该图在较低的限制下，随着填充因子的降低，众多晶体-FQHE液体转变。
The nature of the state at low Landau-level filling factors has been a longstanding puzzle in the field of the fractional quantum Hall effect. While theoretical calculations suggest that a crystal is favored at filling factors $ν\lesssim 1/6$, experiments show, at somewhat elevated temperatures, minima in the longitudinal resistance that are associated with fractional quantum Hall effect at $ν=$ 1/7, 2/11, 2/13, 3/17, 3/19, 1/9, 2/15 and 2/17, which belong to the standard sequences $ν=n/(6n\pm 1)$ and $ν=n/(8n\pm 1)$. To address this paradox, we investigate the nature of some of the low-$ν$ states, specifically $ν=1/7$, $2/13$, and $1/9$, by variational Monte Carlo, density matrix renormalization group, and exact diagonalization methods. We conclude that in the thermodynamic limit, these are likely to be incompressible fractional quantum Hall liquids, albeit with strong short-range crystalline correlations. This suggests a natural explanation for the experimentally observed behavior and a rich phase diagram that admits, in the low-disorder limit, a multitude of crystal-FQHE liquid transitions as the filling factor is reduced.
