Read-Rezayi态和anti-Read-Rezayi态的准粒子凝聚体
Quasiparticle agglomerates in Read-Rezayi and anti Read-Rezayi state
摘要：
我们计算了$k$能级（$k\in\mathbb{N}$）Read-Rezayi（RR）态及其粒子-空穴共轭（反Read-Rezayi（$\bar{\textrm{RR}}$））的主要激发态。这些状态应该建立在第二朗道水平上，总填充因子为$ν=2+ν^*$，RR为$ν^*=k/(k+2)$，$\bar{\textrm{RR}}$为$ν^*=2/(k+2)$。在$k$能级RR态中，基于$\mathbb{Z}_k$赝费米子，主要激发是带有分数电荷的基本准粒子$e^*_k= e/(k + 2)$，其中$e$是电子电荷，如果$k=2,3$ .对于k=4的单qp和2-附聚物，与电荷$2e^*_k$，具有相同的缩放和两者占主导地位，而对于$k>4$的2-附聚物占主导地位。无论如何，2-附聚物的优势可以受到环境重整化的影响。对于所有的$k$ -级$\bar{\textrm{RR}}$状态，单qp和2-凝聚体具有相同的标度并且都占主导地位。在这种情况下，只有环境重整化的存在才能使一个对另一个占优势。我们确定的条件下，环境重整化的带电和中性模式，使占主导地位的阿贝尔2-团聚体的非阿贝尔单准粒子在两个模型和任何值的$k$。我们的结论是，观察，根据这些预测，占主导地位的2-附聚物，在非常低的能量为$ν=5/2$，可以是一个有趣的迹象，支持的有效性的反Pfiranan模型相比，Pfiranan。
英文摘要：
We calculate the dominant excitations for the $k$-level ($k\in\mathbb{N}$) Read-Rezayi (RR) states and their particle-hole conjugates, the anti Read-Rezayi ($\bar{\textrm{RR}}$), proposed for quantum Hall states. These states are supposed to be build over the second Landau level with total filling factor $ν=2+ν^*$ with $ν^*=k/(k+2)$ for RR and $ν^*=2/(k+2)$ for $\bar{\textrm{RR}}$. In the $k$-level RR states, based on $\mathbb{Z}_k$ parafermions, the dominant excitations are the fundamental quasiparticles with fractional charge $e^*_k= e/(k + 2)$, with $e$ the electron charge, if $k=2,3$. For k=4 the single-qp and the 2-agglomerate, with charge $2e^*_k$, have the same scaling and both dominate, while for $k>4$ the 2-agglomerates are dominant. Anyway the dominance of the 2-agglomerates can be affected by the presence of environmental renormalizations. For all the $k$-level $\bar{\textrm{RR}}$ states the single-qp and the 2-agglomerate have the same scaling and both dominate. In this case only the presence of environmental renormalizations can make one dominant over the other. We determine the conditions where the environmental renormalizations of the charged and neutral modes make dominant the Abelian 2-agglomerates over the non-Abelian single-quasiparticles in the two models and for any value of $k$. We conclude observing that, according these predictions, the dominance of 2-agglomerates, at very low energies for the $ν=5/2$, can be an interesting indication supporting the validity of the anti-Pfaffian model in comparison to the Pfaffian.
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