Surveying the quantum group symmetries of integrable open spin chains

Author(s)

Nepomechie, I, Rafael ; Retore, Ana L. ^{[1, 2]}

Affiliation

^[1] Univ Estadual Paulista, Inst Fis Teor, Rua Dr Bento Teobaldo Ferraz 271, Bloco 2, BR-01140070 Sao Paulo - Brazil

^[2] Nepomechie, Rafael, I, Univ Miami, Phys Dept, POB 248046, Coral Gables, FL 33124 - USA

• Document type: Journal article
• Source: Nuclear Physics B; v. 930, p. 91-134, MAY 2018.
• Web of Science Citations: 4

Abstract

Using anisotropic R-matrices associated with affine Lie algebras (g) over cap (specifically, A(2n)((2)), A(2n-1)((2)), B-n((1)),C-n((1)),D-n((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 (g) over cap. We show that these transfer matrices also have a duality symmetry (for the cases C-n((1)) and D-n((1)) ) and additional Z(2) symmetries that map complex representations to their conjugates (for the cases A(2n-1)((2)), B-n(1) and D-n((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. (C) 2018 The Author(s). Published by Elsevier B.V. (AU)

• FAPESP's process: 15/00025-9 - Backlund transformations in integrable hierarchies, solitons and integrable defects
• Grantee: Ana Lúcia Retore
• Support Opportunities: Scholarships in Brazil - Doctorate
• FAPESP's process: 17/03072-3 - Quantum Group Symmetries for A_(2n-1)^(2) models
• Grantee: Ana Lúcia Retore
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate