TY - JOUR
T1 - Surveying the quantum group symmetries of integrable open spin chains
AU - Nepomechie, Rafael I.
AU - Retore, Ana L.
N1 - Funding Information:
We thank J.F. Gomes and M. Jimbo for helpful correspondence. RN was supported in part by a Cooper fellowship, and AR was supported by the São Paulo Research Foundation FAPESP under the process # 2017/03072-3 and # 2015/00025-9 . AR thanks the University of Miami for its warm hospitality.
Funding Information:
We thank J.F. Gomes and M. Jimbo for helpful correspondence. RN was supported in part by a Cooper fellowship, and AR was supported by the São Paulo Research Foundation FAPESP under the process # 2017/03072-3 and # 2015/00025-9. AR thanks the University of Miami for its warm hospitality.
PY - 2018/5
Y1 - 2018/5
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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U2 - 10.1016/j.nuclphysb.2018.02.023
DO - 10.1016/j.nuclphysb.2018.02.023
M3 - Article
AN - SCOPUS:85042909214
VL - 930
SP - 91
EP - 134
JO - Nuclear Physics B
JF - Nuclear Physics B
SN - 0550-3213
ER -