Q-operators for the open Heisenberg spin chain

Abstract

We construct Q-operators for the open spin-1/2 XXX Heisenberg spin chain with diagonal boundary matrices. The Q-operators are defined as traces over an infinite-dimensional auxiliary space involving novel types of reflection operators derived from the boundary Yang-Baxter equation. We argue that the Q-operators defined in this way are polynomials in the spectral parameter and show that they commute with transfer matrix. Finally, we prove that the Q-operators satisfy Baxter's TQ-equation and derive the explicit form of their eigenvalues in terms of the Bethe roots.

23 pages, 1 figure; v2: refs added, minor changes; v3: refs added, summary and text improved

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Cited by in corpus (17)

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• Non-compact quantum spin chains as integrable stochastic particle processes
• Asymptotic representations of augmented q-Onsager algebra and boundary K-operators related to Baxter Q-operators
• Q-systems with boundary parameters
• A note on $q$-oscillator realizations of $U_q(gl(M|N))$ for Baxter $Q$-operators
• Towards the solution of an integrable $D_2^{(2)}$ spin chain
• Universal Baxter TQ-relations for open boundary quantum integrable systems
• A Q-operator for open spin chains I: Baxter's TQ relation
• Baxter operators and asymptotic representations
• Evaluation of the operatorial Q-system for non-compact super spin chains
• On diagonal solutions of the reflection equation
• Generic triangular solutions of the reflection equation: $U_q(\widehat{s{l}_2})$ case
• Scaling limit of the staggered six-vertex model with $U_q(\mathfrak{sl}(2))$ invariant boundary conditions
• Boundary Perimeter Bethe Ansatz
• Spectrum-preserving deformations of integrable spin chains with open boundaries
• Algebraic Bethe ansatz for Q-operators of the open XXX Heisenberg chain with arbitrary spin
• On Exceptional 't Hooft Lines in 4D-Chern-Simons Theory