Lieb-Robinson Bounds in Long-Range Bosonic Systems

Abstract:
In the early 1970s, Lieb and Robinson proved that for a special class of quantum systems, the speed of information propagation is bounded. This result is captured by the so-called Lieb-Robinson bounds (LRB). Since then, LRB have become a fundamental tool in the mathematical analysis of quantum many-body systems, motivating substantial efforts to extend them to more general settings. In this talk, I will discuss LRB for bosonic lattice systems with long-range interactions. These systems present two major challenges: 1) long-range interactions (e.g., those that decay polynomially) are difficult to handle mathematically, 2) bosonic systems involve unbounded interactions, complicating their analysis. The main ingredients for the proof are long-range particle propagation bounds, which control the transport of bosons. In the talk, I will discuss how they can be combined with known LRB for bounded interactions to derive LRB in the bosonic setting. The talk is based on joint work with Tomotaka Kuwahara and Cheng Shang.