TY - JOUR

T1 - Algebraic Bethe ansatz for the quantum group invariant open XXZ chain at roots of unity

AU - Gainutdinov, Azat M.

AU - Nepomechie, Rafael I.

N1 - Funding Information:
AMG thanks Hubert Saleur for valuable discussions, and the IPhT in Saclay for its hospitality. The work of AMG was supported by DESY and Humboldt fellowships, Centre National de la Recherche Scientifique and RFBR -grant 13-01-00386 . RN thanks Rodrigo Pimenta and Vitaly Tarasov for valuable discussions, and the DESY theory group for its hospitality. The work of RN was supported in part by the National Science Foundation under Grant PHY-1212337 , and by a Cooper fellowship .
Publisher Copyright:
© 2016 The Author(s)

PY - 2016/8/1

Y1 - 2016/8/1

N2 - 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.

AB - 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.

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U2 - 10.1016/j.nuclphysb.2016.06.007

DO - 10.1016/j.nuclphysb.2016.06.007

M3 - Article

AN - SCOPUS:84975295231

VL - 909

SP - 796

EP - 839

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

ER -