Algebraic Bethe ansatz for the quantum group invariant open XXZ chain at roots of unity

Azat M. Gainutdinov, Rafael Nepomechie

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

For generic values of q, all the eigenvectors of the transfer matrix of the Uqsl(2)-invariant open spin-1/2 XXZ chain with finite length N can be constructed using the algebraic Bethe ansatz (ABA) formalism of Sklyanin. However, when q is a root of unity ([Formula presented] with integer [Formula presented]), the Bethe equations acquire continuous solutions, and the transfer matrix develops Jordan cells. Hence, there appear eigenvectors of two new types: eigenvectors corresponding to continuous solutions (exact complete p-strings), and generalized eigenvectors. We propose general ABA constructions for these two new types of eigenvectors. We present many explicit examples, and we construct complete sets of (generalized) eigenvectors for various values of p and N.

Original languageEnglish (US)
Pages (from-to)796-839
Number of pages44
JournalNuclear Physics B
Volume909
DOIs
StatePublished - Aug 1 2016

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unity
eigenvectors
Jordan
integers
strings
formalism
cells

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

Cite this

Algebraic Bethe ansatz for the quantum group invariant open XXZ chain at roots of unity. / Gainutdinov, Azat M.; Nepomechie, Rafael.

In: Nuclear Physics B, Vol. 909, 01.08.2016, p. 796-839.

Research output: Contribution to journalArticle

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