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.
Highlights
The emergence of statistical physics from unitary quantum dynamics has been debated since the early days of quantum theory [1]
We show that correlations induced by orthonormality between random wave-functions must be taken into account to obtain a consistent derivation of the eigenstate thermalization hypothesis (ETH) from random matrix theory (RMT)
The form obtained for matrix elements of observables is in agreement with the ETH
Summary
We derive the eigenstate thermalization hypothesis (ETH) from a random matrix Hamiltonian by licence. We show that a common assumption in the analysis of quantum chaotic systems, namely the author(s) and the title of the work, journal citation treatment of eigenstates as independent random vectors, leads to inconsistent results. 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. The analytic results are compared to exact diagonalizations of a quantum spin chain for different physical observables in multiple parameter regimes
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
