Baxter's Q-operator is generally believed to be the most powerful tool for the exact diagonalization of integrable models. Curiously, it has hitherto not yet been properly constructed in the simplest such system, the compact spin-1/2 Heisenberg-Bethe XXX spin chain. Here we attempt to fill this gap and show how two linearly independent operatorial solutions to Baxter's TQ equation may be constructed as commuting transfer matrices if a twist field is present. The latter are obtained by tracing over infinitely many oscillator states living in the auxiliary channel of an associated monodromy matrix. We furthermore compare our approach to and differentiate it from earlier articles addressing the problem of the construction of the Q-operator for the XXX chain. Finally we speculate on the importance of Q-operators for the physical interpretation of recent proposals for the Y-system of AdS/CFT. © 2010 IOP Publishing Ltd and SISSA.

A shortcut to the Q-operator / Bazhanov, V. V.; Lukowski, T.; Meneghelli, C.; Staudacher, M.. - In: JOURNAL OF HIGH ENERGY PHYSICS. - ISSN 1029-8479. - (2010). [10.1088/1742-5468/2010/11/P11002]

A shortcut to the Q-operator

Meneghelli C.;
2010

Abstract

Baxter's Q-operator is generally believed to be the most powerful tool for the exact diagonalization of integrable models. Curiously, it has hitherto not yet been properly constructed in the simplest such system, the compact spin-1/2 Heisenberg-Bethe XXX spin chain. Here we attempt to fill this gap and show how two linearly independent operatorial solutions to Baxter's TQ equation may be constructed as commuting transfer matrices if a twist field is present. The latter are obtained by tracing over infinitely many oscillator states living in the auxiliary channel of an associated monodromy matrix. We furthermore compare our approach to and differentiate it from earlier articles addressing the problem of the construction of the Q-operator for the XXX chain. Finally we speculate on the importance of Q-operators for the physical interpretation of recent proposals for the Y-system of AdS/CFT. © 2010 IOP Publishing Ltd and SISSA.
A shortcut to the Q-operator / Bazhanov, V. V.; Lukowski, T.; Meneghelli, C.; Staudacher, M.. - In: JOURNAL OF HIGH ENERGY PHYSICS. - ISSN 1029-8479. - (2010). [10.1088/1742-5468/2010/11/P11002]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11381/2914578
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