RQC Seminar

291st RQC Seminar

• Speaker

  Mr. Xin-Hai Tong
  ( University of Tokyo )

• Date

  15:00-17:00, (3:00 p.m.- 5:00 p.m.) Friday, July 3, 2026

• Venue

  Hybrid( Zoom,
  435-437 Seminar Room, 4F, Main Research Building, Wako Campus / 和光地区 研究本館4階 セミナー室 (435-437) (C01))

• Title

  Clustering Theorem for Bose-Hubbard class Gibbs states

• Inquiries

  tomotaka.kuwahara[at]riken.jp

Abstract
Away from criticality, the exponential clustering of spatial correlation functions is a fundamental property of locally interacting lattice models. While well-established for quantum spin and fermionic systems with finite-dimensional local Hilbert spaces (starting from the seminal work of Araki [1]), analogous results for bosonic systems remain a long-standing open problem. The main difficulty stems from their infinite-dimensional local Hilbert spaces and the unboundedness of relevant operators. This talk presents our recent advance [2] on the clustering theorem for the high-temperature Bose-Hubbard class of Hamiltonians. I will review the history of this problem, introduce our novel methodology, and outline the key steps of the proof. If time permits, I will also discuss further developments [3] and open questions, highlighting the interplay between operator algebras and lattice bosons [4].
Reference:
[1] Huzihiro Araki. Communications in Mathematical Physics, 14:120–157, 1969.
[2] Xin-Hai Tong, Tomotaka Kuwahara and Zongping Gong. arXiv: 2411.10759v4 (2024). To appear in Communications in Mathematical Physics.
[3] Xin-Hai Tong and Tomotaka Kuwahara. arXiv: 2509.25572v2 (2025).
[4] Andreas Deuchert, Jonas Lampart and Marius Lemm. arXiv: 2505.13170v3 (2025).