Nakerst, Goran and Haque, Masudul (2021) Eigenstate thermalization scaling in approaching the classical limit. Physical Review E, 103 (4). ISSN 1539-3755

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Abstract

According to the eigenstate thermalization hypothesis (ETH), the eigenstate-to-eigenstate fluctuations of expectation values of local observables should decrease with increasing system size. In approaching the thermodynamic limit—the number of sites and the particle number increasing at the same rate—the fluctuations should scale as ∼ D − 1 / 2 with the Hilbert space dimension D . Here, we study a different limit—the classical or semiclassical limit—by increasing the particle number in fixed lattice topologies. We focus on the paradigmatic Bose-Hubbard system, which is quantum-chaotic for large lattices and shows mixed behavior for small lattices. We derive expressions for the expected scaling, assuming ideal eigenstates having Gaussian-distributed random components. We show numerically that, for larger lattices, ETH scaling of physical midspectrum eigenstates follows the ideal (Gaussian) expectation, but for smaller lattices, the scaling occurs via a different exponent. We examine several plausible mechanisms for this anomalous scaling.

Item Type:	Article
Keywords:	Eigenstate thermalization scaling; classical limit;
Academic Unit:	Faculty of Science and Engineering > Theoretical Physics
Item ID:	18427
Identification Number:	https://doi.org/10.1103/PhysRevE.103.042109
Depositing User:	Masud Haque
Date Deposited:	25 Apr 2024 11:03
Journal or Publication Title:	Physical Review E
Publisher:	American Physical Society
Refereed:	Yes
URI:	Publisher
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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