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Quantum Inverse Scattering Method. Selected Topics
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abstract
Four lectures given at Nankai Institute of Mathematics, Tianjin, China, 5--13 April 1991 present an elementary introduction into the quantum integrable models aimed for mathematical physicists and mathematicians. The stress is made on the algebraic aspects of the theory and the problem of determining the spectrum of quantum integrals of motion. The XXX magnetic chain is used as the basic example. Two lectures are devoted to a detailed exposition of the Functional Bethe Ansatz --- a new technique alternative to the Algebraic Bethe Ansatz --- and its relation to the separation of variable method. A possibility to extend FBA to the $SL(3)$ is discussed.
Forward citations
Cited by 3 Pith papers
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Violating the All-or-Nothing Picture of Local Charges in Non-Hermitian Bosonic Chains
Non-Hermitian bosonic chains with symmetric hopping can host k-local charges for selected k only, providing counterexamples to all-or-nothing integrability and showing the Grabowski-Mathieu 3-local test is not universal.
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Rational $Q$-systems for integrable spin chains without $U(1)$ symmetry
A rational Q-system with inhomogeneous QQ-relations is constructed for XXZ spin chains with anti-diagonal twist and non-diagonal boundary fields, and numerically shown to yield all physical solutions.
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On correlation functions of the open XYZ spin 1/2 chain with boundary fields related by a constraint
Exact multiple sums and multiple integrals are derived for elementary correlation-function building blocks of the open XYZ spin-1/2 chain with one constraint on its six boundary fields.
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