Non-Abelian fermionization and the landscape of quantum Hall phases
Non-Abelian fermionization and the landscape of quantum Hall phases
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DOI：
10.1103/physrevb.102.195151
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发表时间：
2020-08
期刊：
影响因子：
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通讯作者：
Hart Goldman;R. Sohal;E. Fradkin
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文献类型：
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作者：
Hart Goldman;R. Sohal;E. Fradkin
最近提出的2+1维非阿贝尔玻色子-费米子对偶理论，将U（k）N与SU（N）-k陈-西蒙斯物质理论联系起来，为从阿贝尔复合粒子理论出发探索非阿贝尔量子霍尔态提供了一个新的平台。在这里，我们专注于对偶相关理论的阿贝尔量子霍尔态的玻色子或费米子的非阿贝尔“复合费米子”部分填充朗道水平的理论。我们表明，这些对偶预测特殊的填充分数，阿贝尔和非阿贝尔复合费米子理论出现能够托管不同的拓扑有序的基态，一个阿贝尔和其他非阿贝尔，$U（k）_2$ Blok-Wen状态。而不是在冲突的二元性，我们认为，这些结果表明意想不到的动态中，红外线和最低朗道水平限制未能跨越二元性。在这种情况下，非阿贝尔拓扑顺序可以不稳定，有利于阿贝尔基态，这表明阿贝尔和非阿贝尔状态之间可能存在一阶相变。我们还将这些结构推广到其他非阿贝尔费米子-费米子对偶，在此过程中获得新的衍生物的各种成对的复合费米子相位使用对偶，包括反Pfweian状态。最后，我们描述了在多层结构中，复合费米子在$N$层上的激子配对也可以产生具有$U（k）_2$拓扑序的Blok-Wen态族。
The recent proposal of non-Abelian boson-fermion dualities in 2+1 dimensions, which morally relate $U(k)_N$ to $SU(N)_{-k}$ Chern-Simons-matter theories, presents a new platform for exploring the landscape of non-Abelian quantum Hall states accessible from theories of Abelian composite particles. Here we focus on dualities relating theories of Abelian quantum Hall states of bosons or fermions to theories of non-Abelian "composite fermions" partially filling Landau levels. We show that these dualities predict special filling fractions where both Abelian and non-Abelian composite fermion theories appear capable of hosting distinct topologically ordered ground states, one Abelian and the other a non-Abelian, $U(k)_2$ Blok-Wen state. Rather than being in conflict with the duality, we argue that these results indicate unexpected dynamics in which the infrared and lowest Landau level limits fail to commute across the duality. In such a scenario, the non-Abelian topological order can be destabilized in favor of the Abelian ground state, suggesting the presence of a phase transition between the Abelian and non-Abelian states that is likely to be first order. We also generalize these constructions to other non-Abelian fermion-fermion dualities, in the process obtaining new derivations of a variety of paired composite fermion phases using duality, including the anti-Pfaffian state. Finally, we describe how, in multilayer constructions, excitonic pairing of the composite fermions across $N$ layers can also generate the family of Blok-Wen states with $U(k)_2$ topological order.