Abstract
Baxter’s Q-operator is generally believed to be the most powerful tool for the exact diagonalization ofintegrable models. Curiously, it has hitherto not yet been properly constructed in thesimplest such system, the compact spin- Heisenberg–Bethe XXX spin chain. Here we attempt to fill this gap and show how two linearly independentoperatorial solutions to Baxter’s TQ equation may be constructed as commutingtransfer matrices if a twist field is present. The latter are obtained by tracing overinfinitely many oscillator states living in the auxiliary channel of an associatedmonodromy matrix. We furthermore compare our approach to and differentiateit from earlier articles addressing the problem of the construction of theQ-operatorfor the XXX chain. Finally we speculate on the importance ofQ-operators for the physical interpretation of recent proposals for theY-system of AdS/CFT.
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