分数量子霍尔态的各向同性到各向异性转变
An Isotropic to Anisotropic Transition in a Fractional Quantum Hall State
摘要：
我们研究了一个新的2+1维阿贝尔规范理论，它具有令人惊讶的理论和唯象特征。该理论有一个电场平方的消失系数$e_i^2$，具有动力学临界指数$z=2$的量子临界点的特征，以及一个水平- $k$ Chern-Simons耦合，在这个临界点是{ \it边际}。对于$k=0$，这个理论与描述量子Lifshitz跃迁的自由$z=2$标量场理论是对偶的，但是$k \neq 0$使得标量描述是非定域的。$k \neq 0$理论表现出介于（拓扑）纯陈-西蒙斯理论和标量理论之间的性质。例如，陈-西蒙斯项并不使规范场具有质量。然而，当理论被放置在一个有边界的空间时，有手征边缘模式，和一个非平凡的基态简并$k^g$，当它被放置在一个有限大小的黎曼曲面亏格$g$。$e_i^2$的系数是唯一相关的耦合;它通过各向同性分数量子霍尔态和各向异性分数量子霍尔态之间的量子相变来调谐系统。我们计算在这两个阶段和在临界点的零温度输运系数，并简要评论我们的结果的相关性，最近的实验。
英文摘要：
We study a novel abelian gauge theory in 2+1 dimensions which has surprising theoretical and phenomenological features. The theory has a vanishing coefficient for the square of the electric field $e_i^2$, characteristic of a quantum critical point with dynamical critical exponent $z=2$, and a level-$k$ Chern-Simons coupling, which is {\it marginal} at this critical point. For $k=0$, this theory is dual to a free $z=2$ scalar field theory describing a quantum Lifshitz transition, but $k \neq 0$ renders the scalar description non-local. The $k \neq 0$ theory exhibits properties intermediate between the (topological) pure Chern-Simons theory and the scalar theory. For instance, the Chern-Simons term does not make the gauge field massive. Nevertheless, there are chiral edge modes when the theory is placed on a space with boundary, and a non-trivial ground state degeneracy $k^g$ when it is placed on a finite-size Riemann surface of genus $g$. The coefficient of $e_i^2$ is the only relevant coupling; it tunes the system through a quantum phase transition between an isotropic fractional quantum Hall state and an anisotropic fractional quantum Hall state. We compute zero-temperature transport coefficients in both phases and at the critical point, and comment briefly on the relevance of our results to recent experiments.
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