Off-diagonal observable elements from random matrix theory: distributions, fluctuations, and eigenstate thermalization

Nation, Charlie and Porras, Diego (2018) Off-diagonal observable elements from random matrix theory: distributions, fluctuations, and eigenstate thermalization. New Journal of Physics, 20 (10). 103003 1-25. ISSN 1367-2630

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Abstract

We 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.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Physics and Astronomy
Research Centres and Groups: Atomic, Molecular and Optical Physics Research Group
Subjects: Q Science > QC Physics > QC0170 Atomic physics. Constitution and properties of matter Including molecular physics, relativity, quantum theory, and solid state physics > QC0174.12 Quantum theory. Quantum mechanics
Depositing User: Charlie Nation
Date Deposited: 06 Dec 2018 11:31
Last Modified: 06 Dec 2018 11:32
URI: http://srodev.sussex.ac.uk/id/eprint/80630

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