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arXiv · 2303.10213

Late-time universal distribution functions of observables in one-dimensional many-body quantum systems

I. Vallejo-Fabila·E. Jonathan Torres-Herrera
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Abstract

We study the probability distribution function of the long-time values of observables being time-evolved by Hamiltonians modeling clean and disordered one-dimensional chains of many spin-1/2 particles. In particular, we analyze the return probability and its version for a completely extended initial state, the so-called spectral form factor. We complement our analysis with the spin autocorrelation and connected spin-spin correlation functions, both of interest in experiments with quantum simulators. We show that the distribution function has a universal shape provided the central limit theorem holds. Explicitly, the shape is exponential for the return probability and spectral form factor, meanwhile it is Gaussian for the few-body observables. We also discuss implications over the so-called many-body localization. Remarkably, our approach requires only a single sample of the dynamics and small system sizes, which could be quite advantageous when dealing specially with disordered systems.

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I. Vallejo-Fabila, E. Jonathan Torres-Herrera. 2023-03-17. Late-time universal distribution functions of observables in one-dimensional many-body quantum systems. https://doi.org/10.1103/physreve.108.044102

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