Band Topology of Insulators via the Entanglement Spectrum
Band Topology of Insulators via the Entanglement Spectrum
复制标题
通过纠缠谱了解绝缘体的能带拓扑
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
A. Vishwanath
中科院分区：
文献类型：
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作者：
A. Turner;Yi Zhang;A. Vishwanath
在给定基态波函数的情况下，我们如何唯一地识别量子相？这是许多体理论的关键问题，特别是当我们把相看作拓扑绝缘体时，它们具有相同的对称性，但在拓扑水平上有所不同。纠缠谱已被提出作为捕获特征边缘激发的基态性质。本文研究了拓扑带绝缘子的纠缠谱。我们首先证明具有拓扑表面态的绝缘体在纠缠谱中也必然具有保护模式。然而，令人惊讶的是，反之并非如此。保护纠缠模式也可以出现在没有物理表面状态的绝缘体上，在这种情况下，它们捕获了更难以捉摸的特性。这是通过考虑只具有逆对称的绝缘体来说明的。反转被证明以一种不寻常的方式起作用，作为一个反酉算子，在纠缠谱上，导致这种保护。纠缠简并表明了反转对称绝缘子中各种不同的相位，并且这些相位对相互作用的引入具有鲁棒性。
How do we uniquely identify a quantum phase, given its ground state wave-function? This is a key question for many body theory especially when we consider phases like topological insulators, that share the same symmetry but differ at the level of topology. The entanglement spectrum has been proposed as a ground state property that captures characteristic edge excitations. Here we study the entanglement spectrum for topological band insulators. We first show that insulators with topological surface states will necessarily also have protected modes in the entanglement spectrum. Surprisingly, however, the converse is not true. Protected entanglement modes can also appear for insulators without physical surface states, in which case they capture a more elusive property. This is illustrated by considering insulators with only inversion symmetry. Inversion is shown to act in an unusual way, as an antiunitary operator, on the entanglement spectrum, leading to this protection. The entanglement degeneracies indicate a variety of different phases in inversion symmetric insulators, and these phases are argued to be robust to the introduction of interactions.