Department of Physics, Princeton University, Princeton, New Jersey 08544, USA.
Phys Rev Lett. 2010 May 7;104(18):180502. doi: 10.1103/PhysRevLett.104.180502. Epub 2010 May 3.
We give a complete definition of the entanglement gap separating low-energy, topological levels from high-energy, generic ones, in the "entanglement spectrum" of fractional quantum Hall (FQH) states. This is accomplished by removing the magnetic length inherent in the FQH problem--a procedure which we call taking the conformal limit. The counting of the low-lying entanglement levels starts off as the counting of modes of the edge theory of the FQH state, but quickly develops finite-size effects which we find to serve as a fingerprint of the FQH state. As the sphere manifold where the FQH resides grows, the level spacing of the states at the same angular momentum goes to zero, suggestive of the presence of relativistic gapless edge states. By using the adiabatic continuity of the low-entanglement energy levels, we investigate whether two states are topologically connected.
我们给出了分数量子霍尔（FQH）态“纠缠谱”中低能、拓扑能级与高能、一般能级之间的纠缠能隙的完整定义。这是通过消除 FQH 问题固有的磁长度来实现的——我们称之为取共形极限。低能纠缠能级的计数从 FQH 态边缘理论的模式计数开始，但很快就会出现有限尺寸效应，我们发现这些效应是 FQH 态的特征。随着 FQH 所在的球流形的增长，相同角动量的态的能隙间隔趋于零，表明存在相对论无间隙边缘态。我们利用低纠缠能级的绝热连续性来研究两个态是否在拓扑上是相连的。
