Abstract
Using anisotropic R-matrices associated with affine Lie algebras gˆ (specifically, A2n (2), A2n−1 (2), Bn (1), Cn (1), Dn (1)) and suitable corresponding K-matrices, we construct families of integrable open quantum spin chains of finite length, whose transfer matrices are invariant under the quantum group corresponding to removing one node from the Dynkin diagram of gˆ. We show that these transfer matrices also have a duality symmetry (for the cases Cn (1) and Dn (1)) and additional Z2 symmetries that map complex representations to their conjugates (for the cases A2n−1 (2), Bn (1) and Dn (1)). A key simplification is achieved by working in a certain “unitary” gauge, in which only the unbroken symmetry generators appear. The proofs of these symmetries rely on some new properties of the R-matrices. We use these symmetries to explain the degeneracies of the transfer matrices.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 91-134 |
| Number of pages | 44 |
| Journal | Nuclear Physics B |
| Volume | 930 |
| DOIs | |
| State | Published - May 1 2018 |
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ASJC Scopus subject areas
- Nuclear and High Energy Physics
Cite this
Surveying the quantum group symmetries of integrable open spin chains. / Nepomechie, Rafael; Retore, Ana L.
In: Nuclear Physics B, Vol. 930, 01.05.2018, p. 91-134.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Surveying the quantum group symmetries of integrable open spin chains
AU - Nepomechie, Rafael
AU - Retore, Ana L.
PY - 2018/5/1
Y1 - 2018/5/1
N2 - Using anisotropic R-matrices associated with affine Lie algebras gˆ (specifically, A2n (2), A2n−1 (2), Bn (1), Cn (1), Dn (1)) and suitable corresponding K-matrices, we construct families of integrable open quantum spin chains of finite length, whose transfer matrices are invariant under the quantum group corresponding to removing one node from the Dynkin diagram of gˆ. We show that these transfer matrices also have a duality symmetry (for the cases Cn (1) and Dn (1)) and additional Z2 symmetries that map complex representations to their conjugates (for the cases A2n−1 (2), Bn (1) and Dn (1)). A key simplification is achieved by working in a certain “unitary” gauge, in which only the unbroken symmetry generators appear. The proofs of these symmetries rely on some new properties of the R-matrices. We use these symmetries to explain the degeneracies of the transfer matrices.
AB - Using anisotropic R-matrices associated with affine Lie algebras gˆ (specifically, A2n (2), A2n−1 (2), Bn (1), Cn (1), Dn (1)) and suitable corresponding K-matrices, we construct families of integrable open quantum spin chains of finite length, whose transfer matrices are invariant under the quantum group corresponding to removing one node from the Dynkin diagram of gˆ. We show that these transfer matrices also have a duality symmetry (for the cases Cn (1) and Dn (1)) and additional Z2 symmetries that map complex representations to their conjugates (for the cases A2n−1 (2), Bn (1) and Dn (1)). A key simplification is achieved by working in a certain “unitary” gauge, in which only the unbroken symmetry generators appear. The proofs of these symmetries rely on some new properties of the R-matrices. We use these symmetries to explain the degeneracies of the transfer matrices.
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UR - http://www.scopus.com/inward/citedby.url?scp=85042909214&partnerID=8YFLogxK
U2 - 10.1016/j.nuclphysb.2018.02.023
DO - 10.1016/j.nuclphysb.2018.02.023
M3 - Article
VL - 930
SP - 91
EP - 134
JO - Nuclear Physics B
JF - Nuclear Physics B
SN - 0550-3213
ER -