Long-range deformations of arbitrary homogeneous Yang-Baxter integrable spin chains are realized as twists of the quantum group, with the Drinfeld associator encoding the long-range interaction terms up to first order in the deformation parameter.
An Introduction to Yangian Symmetries
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abstract
We review some aspects of the quantum Yangians as symmetry algebras of two-dimensional quantum field theories. The plan of these notes is the following: 1 - The classical Heisenberg model: Non-Abelian symmetries; The generators of the symmetries and the semi-classical Yangians; An alternative presentation of the semi-classical Yangians; Digression on Poisson-Lie groups. 2 - The quantum Heisenberg chain: Non-Abelian symmetries and the quantum Yangians; The transfer matrix and an alternative presentation of the Yangians; Digression on the double Yangians. Talk given at the "Integrable Quantum Field Theories" conference held at Come, Italy , September 13-19, 1992.
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Generalizes the BIZZ recursive procedure and provides sufficient conditions under which auxiliary field deformations of integrable sigma models retain classical Yangian symmetry and Maillet bracket structure.
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The quantum group structure of long-range integrable deformations
Long-range deformations of arbitrary homogeneous Yang-Baxter integrable spin chains are realized as twists of the quantum group, with the Drinfeld associator encoding the long-range interaction terms up to first order in the deformation parameter.
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The classical Yangian symmetry of Auxiliary Field Sigma Models
Generalizes the BIZZ recursive procedure and provides sufficient conditions under which auxiliary field deformations of integrable sigma models retain classical Yangian symmetry and Maillet bracket structure.