Algebraic Bethe ansatz for Q-operators of the open XXX Heisenberg chain with arbitrary spin
arXiv:2208.02197 · doi:10.1088/1751-8121/aca5d3
Abstract
In this note we construct Q-operators for the spin s open Heisenberg XXX chain with diagonal boundaries in the framework of the quantum inverse scattering method. Following the algebraic Bethe ansatz we diagonalise the introduced Q-operators using the fundamental commutation relations. By acting on Bethe off-shell states and explicitly evaluating the trace in the auxiliary space we compute the eigenvalues of the Q-operators in terms of Bethe roots and show that the unwanted terms vanish if the Bethe equations are satisfied.
arXiv comment17 pages
References in corpus (32)
- Reaction-Diffusion Processes, Critical Dynamics and Quantum Chains
- Integrable Structure of Conformal Field Theory III. The Yang-Baxter Relation
- The ODE/IM Correspondence
- A Shortcut to the Q-Operator
- Gauge Theory and Integrability, II
- Gauge Theory and Integrability, I
- Baxter's Relations and Spectra of Quantum Integrable Models
- Heisenberg XXX Model with General Boundaries: Eigenvectors from Algebraic Bethe Ansatz
- Bethe ansatz for the XXX-S chain with non-diagonal open boundaries
- Quantum Group Representations and Baxter Equation
- A Generalized Q-operator for U_q(\hat(sl_2)) Vertex Models
- Why scalar products in the algebraic Bethe ansatz have determinant representation
- Universal R-matrix and functional relations
- Q-operators in the six-vertex model
- Separation of variables for rational gl(n) spin chains in any compact representation, via fusion, embedding morphism and Backlund flow
- QQ-system and Weyl-type transfer matrices in integrable SO(2r) spin chains
- Oscillator versus prefundamental representations II. Arbitrary higher ranks
- Q-operators for the open Heisenberg spin chain
- Asymptotic representations of augmented q-Onsager algebra and boundary K-operators related to Baxter Q-operators
- Q-systems with boundary parameters
- Completeness of Wronskian Bethe equations for rational gl(m|n) spin chains
- Auxiliary matrices for the six-vertex model and the algebraic Bethe ansatz
- Algebraic Bethe Ansatz for U(1) Invariant Integrable Models: The Method and General Results
- Eigenstates of triangularisable open XXX spin chains and closed-form solutions for the steady state of the open SSEP
- Rational Lax matrices from antidominantly shifted extended Yangians: BCD types
- Algebraic Bethe ansatz for U(1) Invariant Integrable Models: Compact and non-Compact Applications
- A Q-operator for open spin chains I: Baxter's TQ relation
- Universal Baxter TQ-relations for open boundary quantum integrable systems
- Evaluation of the operatorial Q-system for non-compact super spin chains
- On diagonal solutions of the reflection equation
- Transfer matrices of rational spin chains via novel BGG-type resolutions
- A tale of two Bethe ansätze