In the conformal field theory (CFT) approach to the quantum Hall effect, the multi-electron wave functions are expressed as correlation functions in certain rational CFTs. While this approach has led to a well-understood description of the fractionally charged quasihole excitations, the quasielectrons have turned out to be much harder to handle. In particular, forming quasielectron states requires non-local operators, in sharp contrast to quasiholes that can be created by local chiral vertex operators. In both cases, the operators are strongly constrained by general requirements of symmetry, braiding and fusion. Here we construct a quasielectron operator satisfying these demands and show that it reproduces known good quasiparticle wave functions, as well as predicts new ones. In particular we propose explicit wave functions for quasielectron excitations of the Moore-Read Pfaffian state. Further, this operator allows us to explicitly express the composite fermion wave functions in the positive Jain series in hierarchical form, thus settling a longtime controversy. We also critically discuss the status of the fractional statistics of quasiparticles in the Abelian hierarchical quantum Hall states, and argue that our construction of localized quasielectron states sheds new light on their statistics. At the technical level we introduce a generalized normal ordering, that allows us to "fuse" an electron operator with the inverse of an hole operator, and also an alternative approach to the background charge needed to neutralize CFT correlators. As a result we get a fully holomorphic CFT representation of a large set of quantum Hall wave functions.
Energy, interaction, and photoluminescence of spin-reversed quasielectrons in fractional quantum Hall systems
研究了分数量子霍尔区二维电子气的能量谱和光致发光谱。本文计算了反自旋准电子（QE $_{\rm R}$ 's）的单粒子性质，以及它们相互作用和与Laughlin准电子（QE's）、准空穴（QH's）相互作用的赝势。基于$_{\rm R}$ -$_{\rm R}$和$_{\rm R}$ -QE排斥的短程特性，在Halfman的分层方案中，假设了填充因子为$ν={4\over11}$和${5\over13}$的部分非极化不可压态.为了描述光致发光，结合$h($ QE $_{\rm R})_n$状态的价空穴$h$和$n$ QE $_{\rm R}$的家庭预测类似于发现较早的分数带电激子$h$ QE $_n$。比较了两个家族的结合能和光学选择规则。发现$h$ QE $_{\rm R}$与暗的$h$ QE相比具有辐射性，并且发现$h($ QE $_{\rm R})_2$与亮的$h$ QE $_2$相比无辐射性。
From an experimental point of view, quasielectrons and quasiholes play very similar roles in the fractional quantum Hall effect. Nevertheless, the theoretical description of quasielectrons is known to be much harder than the one of quasiholes. The problem is that one obtains a singularity in the wavefunction if one tries to naively construct the quasielectron as the inverse of the quasihole. Here, we demonstrate that the same problem does not arise in lattice fractional quantum Hall models. This result allows us to make detailed investigations of the properties of quasielectrons, including the…
Classical constraints on the reduced density matrix of quantum fluids in a single Landau level, termed as local exclusion conditions (LECs) [B. Yang, arXiv:1901.00047], have recently been shown to characterize the ground state of many FQH phases. In this work, we extend the LEC construction to build the elementary excitations, namely quasiholes and quasielectrons, of these FQH phases. In particular, we elucidate the quasihole counting, categorize various types of quasielectrons, and construct their microscopic wave functions. Our extensive numerical calculations indicate that the undressed qua…
The formation and various possible decay processes of neutral and charged excitonic complexes in electronic integral and fractional quantum Hall systems are discussed. The excitonic complexes are bound states of a small number of the relevant negatively and positively charged quasiparticles (e.g., conduction electrons and valence holes, reversed-spin electrons and spin holes, Laughlin quasielectrons and quasiholes, composite fermions) that occur in an electron system under specific conditions (e.g., electron density, well width, electric and magnetic fields, or hydrostatic pressure). The examp…
Advancing a microscopic framework that rigorously unveils the underlying topological hallmarks of fractional quantum Hall (FQH) fluids is a prerequisite for making progress in the classification of strongly-coupled topological matter. Here we advance a second-quantization framework that helps reveal an exact fusion mechanism for particle fractionalization in FQH fluids, and uncover the fundamental structure behind the condensation of non-local operators characterizing topological order in the lowest-Landau-level (LLL). We show the first exact analytic computation of the quasielectron Berry con…
Photoluminescence from fractional quantum Hall systems: Role of separation between electron and hole layers
研究了分数量子霍尔区二维电子气（2DEG）的光致发光（PL）谱随电子层和价空穴层间距$d$的变化.在磁长度$λ$的数量级的$d$处，2DEG对光学注入空穴的响应的突然变化导致PL光谱的完全重建。在$d<λ$，空穴结合一个或两个电子形成中性（$X$）或带电（$X^-$）激子，PL光谱探测这些状态的寿命和结合能，而不是2DEG的原始相关性。在$d>2λ$，取决于填充因子$ν$，空穴从2DEG倍增以形成"不相关“状态$h$，或者结合一个或两个劳克林准电子（QE）以形成分数带电激子$h$ QE或$h$ QE $_2$。严格的光学选择规则的束缚态，和唯一的光学活性原来是$h$，$h$ QE*（一个激发态的黑暗$h$ QE），和$h$ QE $_2$。早期研究中提出的“任意子激子”$h$ QE $_3$在任何$d$值下既不稳定也不辐射。不同状态的稳定性对存在的QE的2DEG的关键依赖解释了在PL光谱中观察到的异常在$ν={1\over3}$和${2\over3}$。
Energy spectra of fractional quantum Hall systems in the presence of a valence hole
研究了分数量子霍尔区二维电子气与光注入价带空穴相互作用的能谱随填充因子$ν$和电子层与空穴层间距$d$的变化. 2DEG对空穴的响应在磁长度$λ$量级的$d$处突然改变。在$d<λ$，空穴结合电子形成中性（$X$）或带电（$X^-$）激子，光致发光（PL）光谱探测这些状态的寿命和结合能，而不是2DEG的原始相关性。“缀饰激子”的图片（其中激子和2DEG之间的相互作用被提出来仅仅是为了提高激子质量）受到质疑。相反，低能量状态解释的劳克林相关的费米子（电子和$X^-$的）和形成的两个组件的不可压缩的流体状态的电子-空穴等离子体。在$d>2λ$处，空穴与2DEG的两个Laughlin准电子（QE）结合以形成分数带电激子$h$ QE $_n$。先前发现的“任意子激子”$h$ QE $_3$在$d$的任何值下都是不稳定的。不同$h$ QE $_n$复合物的稳定性对2DEG中QE的存在的临界依赖性导致在$ν={1\over3}$或${2\over3}$处观察到PL光谱的不连续性。
We motivate a close look on the usefulness of the Gaffnian and Haffnian quasihole manifold (null spaces of the respective model Hamiltonians) for well-known gapped fractional quantum Hall (FQH) phases. The conformal invariance of these subspaces are derived explicitly from microscopic many-body states. The resultant CFT description leads to an intriguing emergent primary field with $h=2,c=0$, and we argue the quasihole manifolds are quantum mechanically well-defined and well-behaved. Focusing on the incompressible phases at $ν=1/3$ and $ν=2/5$, we show the low-lying excitations of the Laughlin…
Degeneracy of non-abelian quantum Hall states on the torus: domain walls and conformal field theory
我们分析了环面上的非阿贝尔Read-Rezayi量子Hall态，在那里很自然地将多体问题映射到一维晶格模型上。在薄环面上--无Tao-Waveless（TT）极限--相互作用多体问题是完全可解的。在填充$ν=\frac k {kM+2}$的Read-Rezayi态被认为是局部排斥$k+1$ -体相互作用的精确基态，并且在TT极限中，这表现为基态流形中的所有态在任何$kM+2$连续位点上都精确地具有$k$粒子。对于$M\neq 0$，这些态的二体关联也意味着在$M$相邻位置上不存在多于一个粒子。分数带电准粒子和准空穴出现作为域壁之间的基态，我们表明，不同的域壁图案的数量引起的非平凡的简并，所需的非阿贝尔统计这些国家。在本文的第二部分中，我们考虑准空穴简并从共形场论（CFT）的角度来看，并显示出畴壁图案的计数映射一对一的CFT计数通过融合规则。此外，我们还将CFT分析推广到了高亏格拓扑。
Let $m$ denote the number of quasielectrons (QEs) in a quantum Hall system containing $N$ particles altogether. We show in several general cases that for systems containing $m$ QEs in a single angular momentum shell above $N-m$ Fermions in an incompressible quantum liquid (IQL) state having filling factor $ν=\frac{1}{3}$ that there always exists a configuration whose symmetric correlation function $G$ is nonzero. This extends recent comparable results concerning the IQL state. As a consequence, one can obtain (explicitly) a configuration having a nonzero $G$ for all $N=8$ particle systems cont…
Topological phases of matter are distinguished by topological invariants, such as Chern numbers and topological spins, that quantize their response to electromagnetic currents and changes of ambient geometry. Intriguingly, in the $ν=2/5$ fractional quantum Hall effect, prominent theoretical approaches -- the composite fermion theory and conformal field theory -- have constructed two distinct states, the Jain composite fermion (CF) state and the Gaffnian state, for which many of the topological indices coincide and even the microscopic ground state wave functions have high overlap with each oth…
In this paper, a series of $ν=2/5$ fractional quantum Hall wave functions are constructed from conformal field theory(CFT). They share the same topological properties with states constructed by Jain's composite fermion approach. Upon exact lowest Landau level(LLL) projection, some of Jain composite fermion states would not survive if constraints on Landau level indices given in the appendices of this paper were not satisfied. By contrast, states constructed from CFT always stay in LLL. These states are characterized by different topological shifts and multibody relative angular momenta. As a b…
Conformal field theory approach to gapless 1D fermion systems and application to the edge excitations of nu = 1/(2p+1) quantum Hall sequences
我们提出了一个全面的研究有效的共形场论（CFT）描述的低能量激发的气体无自旋相互作用费米子在一个圆上的无隙制度（Luttinger液体）。函数技术和模块化的转换属性被用来计算所有的关联函数在有限的大小和在有限的温度。前向散射无序被精确地处理。在此框架内，电荷输运的量子霍尔流体的圆柱上的Laughlin实验进行了审查。边缘激发以上一个给定的体激发描述的扭曲版本的Luttinger有效理论。对应于nu =1/（2 p +1）填充分数的Luttinger CFTs似乎是有理CFTs（RCFT）。生成器的扩展对称代数被确定为边缘费米子的创造者和零化子，从而给出了一个物理意义的RCFT的角度来看，这些序列的边缘激发。
