Some Aspects of Quantum Dynamics in Many-Body Systems with Power-Law Interactions

In this talk, I will discuss two recent works on dynamics of quantum systems with power-law interactions.

In the first half, I describe a proof of a new family of Lieb-Robinson bounds for lattice spin systems with long-range interactions. Our results apply for arbitrary k-body interactions, so long as they decay as a sufficiently rapid power-law with distance. I will discuss what is appropriate notion of light cone in power-law interacting systems, and compare our results with previous works in this light.

In the second half, I describe a proof of the existence of non-equilibrium phases of matter in the prethermal regime of periodically-driven, power-law interacting systems. In this context, we predict the existence of a disorder-free, prethermal discrete time crystal in one dimension -- a phase strictly forbidden for short-range interactions.