Jordan blocks and the Bethe ansatz III: Class 5 model and its symmetries

2023/09/18 by Juan Miguel Nieto García, García, Juan Miguel Nieto · 3 citations
Mathematics · Chemistry · #Algebraic structures and combinatorial models #Advanced Topics in Algebra #Advanced NMR Techniques and Applications

paper · pdf · doi:10.48550/arxiv.2309.10044

Abstract

We study the Hilbert space of the Class 5 model described in arXiv:1904.12005. Despite being integrable, neither its transfer matrix nor its Hamiltonian are diagonalisable, meaning that the usual Algebraic Bethe Ansatz does not provide the full Hilbert space. Instead, we make use of the symmetries of the model to construct the Jordan blocks of the transfer matrix. We also show that the Hamiltonian and the transfer matrix, despite commuting, do not have the same Jordan block structure.

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