Functional Methods for the Solution of One-Dimensional Quantum Systems
Tobias Wirth
Broschiertes Buch

Functional Methods for the Solution of One-Dimensional Quantum Systems

Fusion Hierarchy, Functional Bethe Ansatz and Non-Linear Integral Equations

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The framework of the Quantum Inverse Scattering Method is used to study the hamiltonian of the XXX and XXZ spin chain with general boundary fields. Key ingredient is the underlying algebraic structure which is a combination of the Yang-Baxter algebra and a so-called Reflection algebra including boundary fields of arbitrary direction and strength. For spin chains with diagonal boundary fields this setup has been well studied using algebraic Bethe ansatz and the inverse problem was solved by Kitanine for infinite chain lengths. These results are picked up and generalized to arbitrary lengths usi...