Nation_2018_New_J._Phys._20_103003.pdf (1.6 MB)
Off-diagonal observable elements from random matrix theory: distributions, fluctuations, and eigenstate thermalization
journal contribution
posted on 2023-06-09, 16:09 authored by Charlie Nation, Diego PorrasWe derive the eigenstate thermalization hypothesis (ETH) from a random matrix Hamiltonian by extending the model introduced by Deutsch (1991 Phys. Rev. A 43 2046). We approximate the coupling between a subsystem and a many-body environment by means of a random Gaussian matrix. We show that a common assumption in the analysis of quantum chaotic systems, namely the treatment of eigenstates as independent random vectors, leads to inconsistent results. However, a consistent approach to the ETH can be developed by introducing an interaction between random wave-functions that arises as a result of the orthonormality condition. This approach leads to a consistent form for off-diagonal matrix elements of observables. From there we obtain the scaling of time-averaged fluctuations of generic observables with system size for which we calculate an analytic form in terms of the inverse participation ratio. The analytic results are compared to exact diagonalizations of a quantum spin chain for different physical observables in multiple parameter regimes.
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Publication status
- Published
File Version
- Published version
Journal
New Journal of PhysicsISSN
1367-2630Publisher
IOP PublishingExternal DOI
Issue
10Volume
20Page range
103003 1-25Department affiliated with
- Physics and Astronomy Publications
Research groups affiliated with
- Atomic, Molecular and Optical Physics Research Group Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2018-12-06First Open Access (FOA) Date
2018-12-06First Compliant Deposit (FCD) Date
2018-12-05Usage metrics
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