A <i>Q</i>-operator for open spin chains I. Baxter’s TQ relation
Bart Vlaar, Robert Weston
Abstract
We construct a Q -operator for the open XXZ Heisenberg quantum spin chain with diagonal boundary conditions and give a rigorous derivation of Baxter’s TQ relation. Key roles in the theory are played by a particular infinite-dimensional solution of the reflection equation and by short exact sequences of intertwiners of the standard Borel subalgebras of U q ( s l ^ 2 ) . The resulting Bethe equations are the same as those arising from Sklyanin’s algebraic Bethe ansatz.
Topics & Concepts
Reflection (computer programming)Chain (unit)Bethe ansatzSpin (aerodynamics)Boundary (topology)MathematicsRelation (database)Boundary value problemAlgebraic numberQuantumYang–Baxter equationMathematical physicsPhysicsQuantum mechanicsConstruct (python library)Heisenberg modelIdeal (ethics)Integrable systemQuantum inverse scattering methodBethe latticeAlgebraic equationSpectrum (functional analysis)Pure mathematicsAlgebraic structures and combinatorial modelsAdvanced Topics in AlgebraHomotopy and Cohomology in Algebraic Topology