Evolution of entanglement spectra under random unitary dynamics
Po-Yao Chang, Xiao Chen, Sarang Gopalakrishnan, J. H. Pixley · arXiv (Cornell University) · 2018
The early stages of the approach to equilibrium in closed quantum systems are not well understood: even when systems are far from full thermalization, one expects local thermalization to occur. We characterize this by exploring the evolution of the entanglement spectrum under various quantum circuits. We find universal features in the entanglement spectrum, which capture this distinction between local and global thermalization. The local structure is captured by the adjacent-level statistics, described by the random matrix theory on O(1) timescales independent of subsystem size; the global structure, captured by the density of states of the reduced density matrix, does not resemble random-matrix predictions and instead follows a scale-free $1/f$ distribution. These features hold for random unitary circuits with and without a conservation law, as well as localized Floquet circuits. We provide a heuristic explanation of our results.