The Commutativity of Integrals of Motion for Quantum Spin Chains and Elliptic Functions Identities

We prove the commutativity of the first two nontrivial integrals of motion for quantum spin chains with elliptic form of the exchange interaction. We also show thair linear independence for the numbers of spins larger than 4. As a byproduct, we obtained several identities between elliptic Weierstras...

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Bibliographic Details
Published inarXiv.org
Main Authors Dittrich, J, Inozemtsev, V I
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 13.11.2007
Subjects
Chains
Commutativity
Elliptic functions
Integrals
Mathematics - Mathematical Physics
Physics - Mathematical Physics
Weierstrass functions
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Summary:We prove the commutativity of the first two nontrivial integrals of motion for quantum spin chains with elliptic form of the exchange interaction. We also show thair linear independence for the numbers of spins larger than 4. As a byproduct, we obtained several identities between elliptic Weierstrass functions of three and four arguments.
ISSN:2331-8422
DOI:10.48550/arxiv.0711.1973