Entanglement Complexity in Quantum Many-Body Dynamics, Thermalization and Localization
Entanglement Complexity in Quantum Many-Body Dynamics, Thermalization and Localization
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量子多体动力学、热化和局域化中的纠缠复杂性
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
C. Chamon
中科院分区：
文献类型：
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作者：
Zhi;A. Hamma;S. Giampaolo;E. Mucciolo;C. Chamon
纠缠通常用冯·诺依曼熵来量化，但它的性质比用单个数字可以表达的要复杂得多。我们证明了三个不同的动力学阶段，即热化、安德森局域化和多体局域化，其特征是量子淬灭后演化的状态的约化密度矩阵光谱的不同模式。虽然纠缠谱显示了安德森局域化情况下的泊松统计，但它显示了多体局域化和热化情况下的普适维格纳-戴森统计，尽管在这两种情况下，普适分布是在非常不同的时间尺度内渐近达到的。我们进一步表明，纠缠的复杂性是通过类 Metropolis 算法解开状态的可能性所揭示的，它是通过纠缠谱级间距是泊松分布还是维格纳-戴森分布来表示的。
Entanglement is usually quantified by von Neumann entropy, but its properties are much more complex than what can be expressed with a single number. We show that the three distinct dynamical phases known as thermalization, Anderson localization, and many-body localization are marked by different patterns of the spectrum of the reduced density matrix for a state evolved after a quantum quench. While the entanglement spectrum displays Poisson statistics for the case of Anderson localization, it displays universal Wigner-Dyson statistics for both the cases of many-body localization and thermalization, albeit the universal distribution is asymptotically reached within very different time scales in these two cases. We further show that the complexity of entanglement, revealed by the possibility of disentangling the state through a Metropolis-like algorithm, is signaled by whether the entanglement spectrum level spacing is Poisson or Wigner-Dyson distributed.