Completeness of Bethe equations

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

HEP - theorymathematical physicsexactly solvable and integrable systems

Audience: researchers in the topic

London Integrability Journal Club

Series comments: To register for this online seminar series please fill the form:

docs.google.com/forms/d/e/1FAIpQLSfIPJS4W5aPu5Cqqy8LoeO0bQkxBMz_5DNhb04vsSWsNz6VAQ/viewform

Announcements also on

integrability-london.weebly.com/