Spread of entanglement and causality
This event is part of the HET Seminar Series.
We investigate causality constraints on the time evolution of entanglement entropy after a global quench in relativistic theories. We first provide a general proof that the so-called tsunami velocity is bounded by the speed of light. We then discuss a free particle streaming model. In more than two spacetime dimensions the spread of entanglement in this model is highly sensitive to the initial entanglement pattern, but we are able to prove an upper bound on the normalized rate of growth of entanglement entropy. The bound is smaller than what one gets for quenches in strongly interacting holographic theories, which highlights the importance of interactions in the spread of entanglement in many-body systems. We propose an interacting model which we believe provides an upper bound on the spread of entanglement for any interacting relativistic theories. In two spacetime dimensions with multiple intervals, this model and its variations are able to reproduce intricate results exhibited by holographic theories for a significant part of the parameter space. Finally, we discuss a model for entanglement propagation based on a tensor network construction for global quenches.