A review showing that quantum spin chains can be solved through classical mKP soliton equations, with a new Bethe-ansatz-free proof of quantum-classical duality.
From Characters to Quantum (Super)Spin Chains via Fusion
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abstract
We give an elementary proof of the Bazhanov-Reshetikhin determinant formula for rational transfer matrices of the twisted quantum super-spin chains associated with the gl(K|M) algebra. This formula describes the most general fusion of transfer matrices in symmetric representations into arbitrary finite dimensional representations of the algebra and is at the heart of analytical Bethe ansatz approach. Our technique represents a systematic generalization of the usual Jacobi-Trudi formula for characters to its quantum analogue using certain group derivatives.
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Classical facets of quantum integrability
A review showing that quantum spin chains can be solved through classical mKP soliton equations, with a new Bethe-ansatz-free proof of quantum-classical duality.