Evolution of entanglement spectra under Rydberg-blockaded dynamics.

Properly identifying and classifying the diverse non-equilibrium phases that isolated quantum many-body systems can exhibit is a major challenge. While focus is generally put on chaotic systems that rapidly thermalize, we investigate a constrained spin system, the so-called PXP model, which weakly breaks ergodicity. For some fine-tuned initial product states the dynamics is anomalously slow and coherence-preserving. We characterize the approach to equilibrium by probing how such initially disentangled state becomes entangled using random matrix-based diagnostics.

Our main result is the onset at very early times of a two-component structure in the evolving entanglement spectrum which remains present at late times. While the small-value component displays a statistical behavior reminiscent of what is observed in generic chaotic systems (i.e. random-matrix like), the large-value component is highly fluctuating at early times and then converges to a surprising power-law form at later times.