Long-range deformations of homogeneous Yang-Baxter integrable spin chains are generated by a twist of the quantum group that produces a non-associative algebra whose Drinfeld associator encodes the long-range terms up to first order.
All regular 4 × 4 solutions of the Yang-Baxter equation
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The authors classify all non-regular 4x4 solutions of the Yang-Baxter equation and prove a correspondence between regular Lax operators and regular solutions, with non-regular cases satisfying a modified equation.
A modified boost-operator method yields new integrable anyonic chains (including su(2)_k spin-3/2, TY(Z_n), Fib×Fib, Fib×Ising) and a criterion for when Temperley-Lieb algebras appear.
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The quantum group structure of long-range integrable deformations
Long-range deformations of homogeneous Yang-Baxter integrable spin chains are generated by a twist of the quantum group that produces a non-associative algebra whose Drinfeld associator encodes the long-range terms up to first order.
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All 4 x 4 solutions of the quantum Yang-Baxter equation
The authors classify all non-regular 4x4 solutions of the Yang-Baxter equation and prove a correspondence between regular Lax operators and regular solutions, with non-regular cases satisfying a modified equation.
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Constrained integrability and anyonic chains
A modified boost-operator method yields new integrable anyonic chains (including su(2)_k spin-3/2, TY(Z_n), Fib×Fib, Fib×Ising) and a criterion for when Temperley-Lieb algebras appear.