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Statistical properties of eigenstate amplitudes in complex quantum systems

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Beugeling,  Wouter
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Baecker,  Arnd
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Moessner,  Roderich
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Haque,  Masudul
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Citation

Beugeling, W., Baecker, A., Moessner, R., & Haque, M. (2018). Statistical properties of eigenstate amplitudes in complex quantum systems. Physical Review E, 98(2): 022204. doi:10.1103/PhysRevE.98.022204.


Cite as: https://hdl.handle.net/21.11116/0000-0002-093F-F
Abstract
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.