Abstract
Integrable open quantum spin-chain transfer matrices constructed from trigonometric R-matrices associated to affine Lie algebras gˆ, and from certain K-matrices (reflection matrices) depending on a discrete parameter p, were recently considered in arXiv:1802.04864 and arXiv:1805.10144. It was shown there that these transfer matrices have quantum group symmetry corresponding to removing the pth node from the gˆ Dynkin diagram. Here we determine the spectrum of these transfer matrices by using analytical Bethe ansatz, and we determine the dependence of the corresponding Bethe equations on p. We propose formulas for the Dynkin labels of the Bethe states in terms of the numbers of Bethe roots of each type. We also briefly study how duality transformations are implemented on the Bethe ansatz solutions.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 266-297 |
| Number of pages | 32 |
| Journal | Nuclear Physics B |
| Volume | 938 |
| DOIs | |
| State | Published - Jan 1 2019 |
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ASJC Scopus subject areas
- Nuclear and High Energy Physics
Cite this
The spectrum of quantum-group-invariant transfer matrices. / Nepomechie, Rafael; Retore, Ana L.
In: Nuclear Physics B, Vol. 938, 01.01.2019, p. 266-297.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - The spectrum of quantum-group-invariant transfer matrices
AU - Nepomechie, Rafael
AU - Retore, Ana L.
PY - 2019/1/1
Y1 - 2019/1/1
N2 - Integrable open quantum spin-chain transfer matrices constructed from trigonometric R-matrices associated to affine Lie algebras gˆ, and from certain K-matrices (reflection matrices) depending on a discrete parameter p, were recently considered in arXiv:1802.04864 and arXiv:1805.10144. It was shown there that these transfer matrices have quantum group symmetry corresponding to removing the pth node from the gˆ Dynkin diagram. Here we determine the spectrum of these transfer matrices by using analytical Bethe ansatz, and we determine the dependence of the corresponding Bethe equations on p. We propose formulas for the Dynkin labels of the Bethe states in terms of the numbers of Bethe roots of each type. We also briefly study how duality transformations are implemented on the Bethe ansatz solutions.
AB - Integrable open quantum spin-chain transfer matrices constructed from trigonometric R-matrices associated to affine Lie algebras gˆ, and from certain K-matrices (reflection matrices) depending on a discrete parameter p, were recently considered in arXiv:1802.04864 and arXiv:1805.10144. It was shown there that these transfer matrices have quantum group symmetry corresponding to removing the pth node from the gˆ Dynkin diagram. Here we determine the spectrum of these transfer matrices by using analytical Bethe ansatz, and we determine the dependence of the corresponding Bethe equations on p. We propose formulas for the Dynkin labels of the Bethe states in terms of the numbers of Bethe roots of each type. We also briefly study how duality transformations are implemented on the Bethe ansatz solutions.
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UR - http://www.scopus.com/inward/citedby.url?scp=85057181774&partnerID=8YFLogxK
U2 - 10.1016/j.nuclphysb.2018.11.017
DO - 10.1016/j.nuclphysb.2018.11.017
M3 - Article
AN - SCOPUS:85057181774
VL - 938
SP - 266
EP - 297
JO - Nuclear Physics B
JF - Nuclear Physics B
SN - 0550-3213
ER -