Beugeling, Wouter and Bäcker, Arnd and Moessner, Roderich and Haque, Masudul (2018) Statistical properties of eigenstate amplitudes in complex quantum systems. Physical Review E, 98 (022204). ISSN 1539-3755

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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.

Item Type:	Article
Keywords:	Eigenstate thermalization; Quantum chaos; 1-dimensional spin chains; Quantum billiards; Bose-Hubbard model; Exact diagonalization;
Academic Unit:	Faculty of Science and Engineering > Mathematical Physics
Item ID:	10558
Identification Number:	https://doi.org/10.1103/PhysRevE.98.022204
Depositing User:	Masud Haque
Date Deposited:	21 Feb 2019 16:59
Journal or Publication Title:	Physical Review E
Publisher:	American Physical Society
Refereed:	Yes
URI:	https://journals.aps.org/pre
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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