An improved Lieb-Robinson bound for many-body Hamiltonians with power-law interactions

The Lieb-Robinson bound limits the velocity of the spread of information in non-relativistic short-range interacting quantum systems, inducing a notion of speed of light. More specifically, it proves that, under time evolution, any local operator remains confined (up to exponentially decaying tails) to a region whose radius grows linearly with time. Motivated by experimental platforms such as ion traps, Rydberg atoms and spin defects in solids, recent work has investigated such bounds in long-range interacting systems, where the interaction strength decays as a power-law of the distance. In these results, the extent of the time evolved local operator is characterized by power-law tails and one obtains a power-law light-cone. In this talk, we introduce a new notion of light-cone for power-law interacting systems that induces a more stringent definition of locality. We prove new Lieb-Robinson bounds for multi-body interacting systems which improve the spatial decay profile of the time evolved local operator and thus lead to a better light-cone. These improvements enable the proof of the existence of a long-lived prethermal regime in long-range interacting systems.