Li Hui, Haldane F D M
Physics Department, Princeton University, Princeton, New Jersey 08544, USA.
Phys Rev Lett. 2008 Jul 4;101(1):010504. doi: 10.1103/PhysRevLett.101.010504. Epub 2008 Jul 3.
We study the "entanglement spectrum" (a presentation of the Schmidt decomposition analogous to a set of "energy levels") of a many-body state, and compare the Moore-Read model wave function for the nu=5/2 fractional quantum Hall state with a generic 5/2 state obtained by finite-size diagonalization of the second-Landau-level-projected Coulomb interactions. Their spectra share a common "gapless" structure, related to conformal field theory. In the model state, these are the only levels, while in the "generic" case, they are separated from the rest of the spectrum by a clear "entanglement gap", which appears to remain finite in the thermodynamic limit. We propose that the low-lying entanglement spectrum can be used as a "fingerprint" to identify topological order.
我们研究了多体状态的“纠缠谱”（类似于一组“能级”的施密特分解表示），并将 ν = 5/2 分数量子霍尔态的摩尔 - 里德模型波函数与通过第二朗道能级投影库仑相互作用的有限尺寸对角化得到的一般 5/2 态进行了比较。它们的谱共享一种与共形场论相关的共同“无隙”结构。在模型态中，这些是唯一的能级，而在“一般”情况下，它们与谱的其余部分由一个明显的“纠缠能隙”分隔开，该能隙在热力学极限下似乎保持有限。我们提出，低能纠缠谱可作为识别拓扑序的“指纹”。
