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arXiv · 1812.04770

Randomness and Chaos in Qubit Models

Pak Hang Chris Lau·Chen-Te Ma·Jeff Murugan·Masaki Tezuka
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Abstract

We introduce randomness into a class of integrable models and study the spectral form factor as a diagnostic to distinguish between randomness and chaos. Spectral form factors exhibit a characteristic dip-ramp-plateau behavior in the $N>2$ SYK$_2$ model at high temperatures that is absent in the $N=2$ SYK$_2$ model. Our results suggest that this dip-ramp-plateau behavior implies the existence of random eigenvectors in a quantum many-body system. To further support this observation, we examine the Gaussian random transverse Ising model and obtain consistent results without suffering from small $N$ issues. Finally, we demonstrate numerically that expectation values of observables computed in a random quantum state at late times are equivalent to the expectation values computed in the thermal ensemble in a Gaussian random one-qubit model.

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Pak Hang Chris Lau, Chen-Te Ma, Jeff Murugan, Masaki Tezuka. 2019-05-12. Randomness and Chaos in Qubit Models. https://doi.org/10.1016/j.physletb.2019.05.052

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