Completeness of Bethe equations

Dmytro Volin (Nordita)

07-May-2020, 09:00-11:00 (4 years ago)

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

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