A Shortcut to the Q-Operator

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 and differentiate our approach to 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.

41 pages, 2 figures; v2: references added; v3: version published in J. Stat. Mech

References in corpus (10)

• Giant Magnons
• Thermodynamic Bethe Ansatz for the AdS_5 x S^5 Mirror Model
• String hypothesis for the AdS_5 x S^5 mirror
• Baxter Q-Operators and Representations of Yangians
• Baxter's Q-operators for supersymmetric spin chains
• Complete 1-loop test of AdS/CFT
• The Baxter's Q-operator for the W-algebra $W_N$
• Analytic theory of the eight-vertex model
• Quantum Stability for the Heisenberg Ferromagnet
• A new Q-matrix in the Eight-Vertex Model

Cited by in corpus (14)

• Quasilocal conservation laws in XXZ spin-1/2 chains: open, periodic and twisted boundary conditions
• Baxter Q-Operators and Representations of Yangians
• Wronskian Solution for AdS/CFT Y-system
• Twisting the Mirror TBA
• Y-system and beta-deformed N=4 Super-Yang-Mills
• Yangians, S-matrices and AdS/CFT
• Q-operators in the six-vertex model
• On the universal R-matrix for the Izergin-Korepin model
• Twisting singular solutions of Bethe's equations
• Introduction to Integrability and One-point Functions in $\mathcal{N}=4$ SYM and its Defect Cousin
• The non-compact XXZ spin chain as stochastic particle process
• From Baxter Q-Operators to Local Charges
• Drinfeld basis for string-inspired Baxter operators
• Antiperiodic XXZ chains with arbitrary spins: Complete eigenstate construction by functional equations in separation of variables