Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany.
Lehrstuhl für Theoretische Physik I & II, Technische Universität Dortmund, Otto-Hahn-Straße 4, 44221 Dortmund, Germany.
Phys Rev E. 2018 Aug;98(2-1):022204. doi: 10.1103/PhysRevE.98.022204.
We study the eigenstates of quantum systems with large Hilbert spaces, via their distribution of wave-function amplitudes in a real-space basis. For single-particle "quantum billiards," these real-space amplitudes are known to have Gaussian distribution for chaotic systems. In this work, we formulate and address the corresponding question for many-body lattice quantum systems. For integrable many-body systems, we examine the deviation from Gaussianity and provide evidence that the distribution generically tends toward power-law behavior in the limit of large sizes. We relate the deviation from Gaussianity to the entanglement content of many-body eigenstates. For integrable billiards, we find several cases where the distribution has power-law tails.
我们通过在实空间基中的波函数幅度分布来研究具有大 Hilbert 空间的量子系统的本征态。对于单粒子“量子台球”，已知这些实空间幅度在混沌系统中具有高斯分布。在这项工作中，我们针对多体晶格量子系统提出并解决了相应的问题。对于可积的多体系统，我们研究了偏离高斯分布的情况，并提供了证据表明，在大尺寸极限下，分布通常趋向于幂律行为。我们将偏离高斯分布与多体本征态的纠缠内容联系起来。对于可积的台球，我们发现了几种分布具有幂律尾部的情况。
