The twisted XXZ chain at roots of unity revisited

Abstract

The symmetries of the twisted XXZ spin-chain (alias the twisted six-vertex model) at roots of unity are investigated. It is shown that when the twist parameter is chosen to depend on the total spin an infinite-dimensional non-abelian symmetry algebra can be explicitly constructed for all spin sectors. This symmetry algebra is identified to be the upper or lower Borel subalgebra of the sl_2 loop algebra. The proof uses only the intertwining property of the six-vertex monodromy matrix and the familiar relations of the six-vertex Yang-Baxter algebra.

10 pages, 2 figures. One footnote and some comments in the conclusions added

References in corpus (7)

• XXZ Bethe states as highest weight vectors of the $s{l}_2$ loop algebra at roots of unity
• Auxiliary matrices for the six-vertex model at roots of 1 and a geometric interpretation of its symmetries
• Auxiliary matrices for the six-vertex model at roots of unity II
• Loop symmetry of integrable vertex models at roots of unity
• The $s{l}_2$ loop algebra symmetry of the twisted transfer matrix of the six vertex model at roots of unity
• Quantum superalgebras at roots of unity and non-abelian symmetries of integrable models
• On Bethe vectors in the XXZ model at roots of unity

Cited by in corpus (11)

• Lack of symmetry restoration after a quantum quench: an entanglement asymmetry study
• Quasilocal conservation laws from semicyclic irreducible representations of $U_q({\mathfrak{sl}}_2)$ in $XXZ$ spin-$1/2$ chains
• From affine Hecke algebras to boundary symmetries
• XXZ Bethe states as highest weight vectors of the $s{l}_2$ loop algebra at roots of unity
• The eight-vertex model and lattice supersymmetry
• Boundary non-local charges from the open spin chain
• Auxiliary matrices for the six-vertex model and the algebraic Bethe ansatz
• A Q-operator for the quantum transfer matrix
• Riemann surfaces for integer counting processes
• Generalized Drinfeld polynomials for highest weight vectors of the Borel subalgebra of the $s{l}_2$ loop algebra
• Extension of a Borel subalgebra symmetry into the sl(2) loop algebra symmetry for the twisted XXZ spin chain at roots of unity and the Onsager algebra