Onset of universality in the dynamical mixing of a pure state

We study the time dynamics of random density matrices generated by evolving the same pure state using a Gaussian orthogonal ensemble (GOE) of Hamiltonians. We show that the spectral statistics of the resulting mixed state is well described by random matrix theory (RMT) and undergoes a crossover from the GOE to the Gaussian unitary ensemble (GUE) for short and large times respectively. Using a semi-analytical treatment relying on a power series of the density matrix as a function of time, we find that the crossover occurs in a characteristic time that scales as the inverse of the Hilbert space dimension. The RMT results are contrasted with a paradigmatic model of many-body localization in the chaotic regime, where the GUE statistics is reached at large times, while for short times the statistics strongly depends on the peculiarity of the considered subspace.

Automated summary

This study investigates the time dynamics of random density matrices generated by evolving the same pure state using a Gaussian orthogonal ensemble (GOE) of Hamiltonians. It is shown that the resulting mixed state exhibits spectral statistics that can be well described by random matrix theory (RMT), undergoing a crossover from GOE to the Gaussian unitary ensemble (GUE) for short and large times, respectively. By employing a semi-analytical treatment based on a power series, the crossover is found to occur in a characteristic time that scales inversely with the Hilbert space dimension. The results from RMT are compared with a paradigmatic model of many-body localization in the chaotic regime, where GUE statistics is reached at large times, while the statistics for short times strongly depend on the specific subspace considered.