3 years ago

Statistical properties of eigenstate amplitudes in complex quantum systems.

Masudul Haque, Roderich Moessner, Arnd Bäcker, Wouter Beugeling

We study the eigenstates of quantum systems with large Hilbert spaces, via their distribution of wavefunction 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.

Publisher URL: http://arxiv.org/abs/1710.11433

DOI: arXiv:1710.11433v1

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