07.05.2020 (Thursday)

Completeness of Bethe equations

Journal Club Dmytro Volin (Uppsala University)

10:00 Other
room Zoom, instructions in abstract

We review a proof of bijection between eigenstates of the Bethe algebra and solutions of Bethe equations written as a Wronskian quantisation condition or as QQ-relations on Young diagrams. Furthermore, it is demonstrated that the Bethe algebra is maximal commutative and it has simple spectrum every time it is diagonalisable. The proof covers rational gl(m|n) spin chains in the defining representation with the famous Heisenberg spin chain being a particular subcase. The proof is rigorous (no general position arguments are used). We do not rely on the string hypothesis and moreover we conjecture a precise meaning of Bethe strings as a consequence of the proposed proof. A short introduction with necessary facts about polynomial rings will be given at the beginning of the talk. Based on 2004.02865 NOTE: Part of London Integrability Journal Club. Please register at integrability-london.weebly.com to participate.