数理物理セミナー: Maximal speed of propagation for lattice bosons under long-range interactions and their applications to Lieb-Robinson bounds. (Carla Rubiliani 氏)

Time： 16:30-17:30

Place：理学部3号館 3-210

Speaker： Carla Rubiliani 氏（チュービンゲン大学）

Title：Maximal speed of propagation for lattice bosons under long-range
interactions and their applications to Lieb-Robinson bounds.

Abstract：In 1972, Lieb and Robinson showed that quantum information propagates
ballistically in systems with local and bounded interactions, a result now known as the Lieb-Robinson bounds (LRBs). Since the early 2000s, Hastings and others have used LRBs as a powerful tool to resolve long-standing open problems in mathematical physics, prompting much work on generalizing them. However, the understanding of LRBs for unbounded interactions remains incomplete. A key example is the Bose-Hubbard model, where standard techniques fail due to boson accumulation. Schuch, Harrison, Osborne, and Eisert suggested that controlling boson transport may be central to extending LRBs in this context. Following this idea, many results have been proved, but long-range unbounded interactions still constitute a big obstacle.

In this talk, I will present a new long-range thermodynamically stable particle propagation bound that could allow proving the first thermodynamically stable Lieb-Robinson bounds for long-range interactions. The main novelty in our proof is a multi-scale adaptation of the adiabatic space-time localisation observable (ASTLO) method, which allows removing the dependence of the error term from far-away particles.

Organizer：宮尾 忠宏（北海道大学）