Physics (Internal)

Aspects of entanglement growth after a quantum quench

This event is part of the Biophysics/Condensed Matter Seminar Series.

The growth of entanglement plays a fundamental role in the process of thermalization in closed quantum systems and has recently become amenable to experimental detection, through the measurement of so-called higher Rényi entropies. In this talk I will show that the behavior of such Rényi entropies can be qualitatively different from that of the theoretically more studied von Neumann entropy; in particular I will argue that the former grow sub-ballistically, as the square root of time, in systems with diffusive transport. I provide evidence for this in both a U(1) symmetric random circuit model and in a non-integrable spin chain, where energy is the sole conserved quantity, and interpret the results as a consequence of local quantum fluctuations in conserved densities. In the second part of the talk I will discuss the dynamics of the entanglement spectrum of small subsystems and use it to identify signatures of the different dynamical velocities that control thermalization. In particular I will show how the onset of level repulsion in the spectrum occurs at different timescales depending on the 'entanglement energy', and relate this to the problem of operator spreading.