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 language | English (US) |
|---|---|
| Pages (from-to) | 796-839 |
| Number of pages | 44 |
| Journal | Nuclear Physics B |
| Volume | 909 |
| DOIs | |
| State | Published - Aug 1 2016 |
Fingerprint
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 journal › Article
}
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
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.
UR - http://www.scopus.com/inward/record.url?scp=84975295231&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84975295231&partnerID=8YFLogxK
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 -