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Numerical studies of quantum entanglement in fractional quantum Hall effect systems.

机译：分数量子霍尔效应系统中量子纠缠的数值研究。

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Fractional quantum Hall effects have attracted broad interest since the phenomena were discovered. In two-dimensions, electron systems subject to perpendicular magnetic fields behave very strangely, appearing to contain fractionally charged particles that obey fractional statistics.;Recently, there has been increasing interest in using quantum entanglement as a probe to detect topological properties of many-body quantum states, in particular the states exhibiting the fractional quantum Hall effect. Among various measures of quantum entanglement, the entanglement entropy has by far been the favorite. It has been shown that the topological entanglement entropy of fractional quantum Hall states is closely related to its topological order.;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 model wavefunction for both the various fractional quantum Hall state with generic states at appropriate filling (nu = 1/3, 5/2 etc) obtained by finite-size diagonalization of the Landau-level-projected Coulomb interactions. Their spectra share a common "gapless" structure, related to conformal field theory. In the model states, 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.;Assuming that the gap does remain finite in the thermodynamic limit, characterization of the entanglement spectrum is a reliable way to identify a topologically ordered state (the low-lying entanglement spectrum can be used as a "fingerprint"). While finite-size numerical studies often show impressive overlaps between model wave-functions and "realistic" states at intermediate system sizes, this cannot persist in the thermodynamic limit. Furthermore, the entanglement spectrum is a property of the ground state wave-function itself, as oppose to the physical excitations of a system with boundaries, so allows direct comparison between model states and physical ones.
机译：自从现象被发现以来，分数量子霍尔效应就引起了广泛的兴趣。在二维中，受到垂直磁场作用的电子系统的行为非常奇怪，似乎包含服从分数统计的带分数电荷的粒子;最近，人们越来越有兴趣使用量子纠缠作为探针来检测多体的拓扑性质量子态，特别是表现出分数量子霍尔效应的态。在量子纠缠的各种度量中，迄今为止，纠缠熵是最喜欢的。研究表明，分数量子霍尔态的拓扑纠缠熵与其拓扑次序密切相关。我们研究了“纠缠谱”，它是施密特分解的一种表示，类似于一组多能级的“能级”。体态，并比较各种分数量子霍尔态的模型波函数与通过兰道能级投影的库仑相互作用的有限尺寸对角化获得的适当填充（nu = 1 / 3、5 / 2等）的一般态的波函数。它们的光谱共享与共形场理论有关的常见“无间隙”结构。在模型状态下，这些是唯一的水平，而在“一般”情况下，它们通过清晰的“纠缠间隙”与光谱的其余部分分开，该纠缠间隙似乎在热力学极限内保持有限。在热力学极限中，间隙确实保持有限，纠缠谱的表征是识别拓扑有序状态的可靠方法（低洼纠缠谱可用作“指纹”）。虽然有限尺寸的数值研究通常显示模型波函数与中间系统尺寸的“现实”状态之间有令人印象深刻的重叠，但这不能在热力学极限中持续存在。此外，纠缠谱是基态波函数本身的一个属性，与具有边界的系统的物理激励相反，因此可以在模型状态和物理状态之间进行直接比较。

著录项

  • 作者

    Li, Hui.;

  • 作者单位

    Princeton University.;

  • 授予单位 Princeton University.;
  • 学科 Physics Condensed Matter.
  • 学位 Ph.D.
  • 年度 2009
  • 页码 107 p.
  • 总页数 107
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 O49;
  • 关键词

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