Statistical properties of eigenstate amplitudes in complex quantum systems
Abstract
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.
Cite
@article{arxiv.1710.11433,
title = {Statistical properties of eigenstate amplitudes in complex quantum systems},
author = {Wouter Beugeling and Arnd Bäcker and Roderich Moessner and Masudul Haque},
journal= {arXiv preprint arXiv:1710.11433},
year = {2018}
}
Comments
revised version, with appendices; 15 pages, 10 figures