A Q-operator for open spin chains I: Baxter's TQ relation

Abstract

We construct a Q-operator for the open XXZ Heisenberg quantum spin chain with diagonal boundary conditions and give a rigorous derivation of Baxter's TQ relation. Key roles in the theory are played by a particular infinite-dimensional solution of the reflection equation and by short exact sequences of intertwiners of the standard Borel subalgebras of $U_q(\widehat{{\mathfrak{sl}}_2})$. The resulting Bethe equations are the same as those arising from Sklyanin's algebraic Bethe ansatz.

arXiv comment42 pages; added more references, corrected some typos, added Appendix D

References in corpus (39)

• Integrable Structure of Conformal Field Theory, Quantum KdV Theory and Thermodynamic Bethe Ansatz
• Integrable Structure of Conformal Field Theory II. Q-operator and DDV equation
• Integrable Structure of Conformal Field Theory III. The Yang-Baxter Relation
• Quantum symmetric Kac-Moody pairs
• Boundary K-matrices for the XYZ, XXZ AND XXX spin chains
• Algebraic Structures Related to Reflection Equations
• A Shortcut to the Q-Operator
• Integrable structure of W_3 Conformal Field Theory, Quantum Boussinesq Theory and Boundary Affine Toda Theory
• Hidden Grassmann Structure in the XXZ Model II: Creation Operators
• The half-infinite XXZ chain in Onsager's approach
• Baxter's Relations and Spectra of Quantum Integrable Models
• Quantum group symmetry in sine-Gordon and affine Toda field theories on the half-line
• Q-operator and T-Q relation from the fusion hierarchy
• Asymptotic representations and Drinfeld rational fractions
• Baxter's Q-operator for the homogeneous XXX spin chain
• Quantum Group Representations and Baxter Equation
• Exercises with the universal R-matrix
• On The Baxter's Q - Operator for the XXX Spin Chain
• The Baxter's Q-operator for the W-algebra $W_N$
• Analytical Bethe Ansatz for $A_{2n-1}^{(2)},B_n^{(1)},C_n^{(1)},D_n^{(1)}$ quantum-algebra-invariant open spin chains
• Bethe Ansatz and Q-operator for the open ASEP
• A Generalized Q-operator for U_q(\hat(sl_2)) Vertex Models
• Cluster algebras and category O for representations of Borel subalgebras of quantum affine algebras
• A Q-Operator Identity for the Correlation Functions of the Infinite XXZ Spin-Chain
• On the boundaries of quantum integrability for the spin-1/2 Richardson-Gaudin system
• Universal integrability objects
• Factorization of the transfer matrices for the quantum sl(2) spin chains and Baxter equation
• Quantum affine reflection algebras of type d_n^(1) and reflection matrices
• Q-operators for the open Heisenberg spin chain
• Auxiliary matrices for the six-vertex model at roots of 1 and a geometric interpretation of its symmetries
• Finite type modules and Bethe ansatz equations
• Braided module categories via quantum symmetric pairs
• Asymptotic representations of augmented q-Onsager algebra and boundary K-operators related to Baxter Q-operators
• Baxter Q-operators of the XXZ chain and R-matrix factorization
• The universal R-matrix and factorization of the L-operators related to the Baxter Q-operators
• Boundary transfer matrices and boundary quantum KZ equations
• Boundary quantum Knizhnik-Zamolodchikov equations and fusion
• Vertex Models and Spin Chains in Formulas and Pictures
• Boundary quantum Knizhnik-Zamolodchikov equations and Bethe vectors

Cited by in corpus (9)

• QQ-system and Weyl-type transfer matrices in integrable SO(2r) spin chains
• Universal Baxter TQ-relations for open boundary quantum integrable systems
• Lax Operator and superspin chains from 4D CS gauge theory
• Tensor K-matrices for quantum symmetric pairs
• Scaling limit of the staggered six-vertex model with $U_q(\mathfrak{sl}(2))$ invariant boundary conditions
• 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
• Universal TT- and TQ-relations via centrally extended q-Onsager algebra
• BC-type open $SL(2,\mathbb{C})$ spin chain