Baxter Q-operator and Separation of Variables for the open SL(2,R) spin chain

Abstract

We construct the Baxter Q-operator and the representation of the Separated Variables (SoV) for the homogeneous open SL(2,R) spin chain. Applying the diagrammatical approach, we calculate Sklyanin's integration measure in the separated variables and obtain the solution to the spectral problem for the model in terms of the eigenvalues of the Q-operator. We show that the transition kernel to the SoV representation is factorized into the product of certain operators each depending on a single separated variable. As a consequence, it has a universal pyramid-like form that has been already observed for various quantum integrable models such as periodic Toda chain, closed SL(2,R) and SL(2,C) spin chains.

29 pages, 9 figures, Latex style

References in corpus (2)

• Noncompact Heisenberg spin magnets from high-energy QCD: I. Baxter Q-operator and Separation of Variables
• Separation of variables for the quantum SL(2,R) spin chain

Cited by in corpus (52)

• Baxter Q-Operators and Representations of Yangians
• New Construction of Eigenstates and Separation of Variables for SU(N) Quantum Spin Chains
• The open XXX spin chain in the SoV framework: scalar product of separate states
• $T$-$Q$ relation and exact solution for the XYZ chain with general nondiagonal boundary terms
• On quantum separation of variables
• Quantum mechanics of null polygonal Wilson loops
• Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra I
• Separated variables and wave functions for rational gl(N) spin chains in the companion twist frame
• R-Matrix and Baxter Q-Operators for the Noncompact SL(N,C) Invariant Spin Chain
• Complete spectrum of quantum integrable lattice models associated to Y(gl(n)) by separation of variables
• On determinant representations of scalar products and form factors in the SoV approach: the XXX case
• Separation of variables for rational gl(n) spin chains in any compact representation, via fusion, embedding morphism and Backlund flow
• Baxter Q-operator for graded SL(2|1) spin chain
• Factorization of the transfer matrices for the quantum sl(2) spin chains and Baxter equation
• Non-compact quantum spin chains as integrable stochastic particle processes
• The open XXZ spin chain in the SoV framework: scalar product of separate states
• Noncompact SL(2,R) spin chain
• Q-operators for the open Heisenberg spin chain
• OPE for null Wilson loops and open spin chains
• Factorization of R-matrix and Baxter Q-operators for generic sl(N) spin chains
• Asymptotic representations of augmented q-Onsager algebra and boundary K-operators related to Baxter Q-operators
• Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra II
• Evolution equation for the higher-twist B-meson distribution amplitude
• On Scalar Products in Higher Rank Quantum Separation of Variables
• Integrability in heavy quark effective theory
• On quantum separation of variables beyond fundamental representations
• Complete spectrum of quantum integrable lattice models associated to ${\mathcal{U}}_q(\widehat{g{l}_n})$ by separation of variables
• Separation of variables bases for integrable $g{l}_{\mathcal{M}|\mathcal{N}}$ and Hubbard models
• Noncompact sl(N) spin chains: BGG-resolution, Q-operators and alternating sum representation for finite dimensional transfer matrices
• On Separation of Variables for Reflection Algebras
• Chiral limit of N = 4 SYM and ABJM and integrable Feynman graphs
• $\mathrm{SL}(2,\mathbb{C})$ Gustafson Integrals
• Correlation functions for open XXZ spin 1/2 quantum chains with unparallel boundary magnetic fields
• Correlation functions by Separation of Variables: the XXX spin chain
• Universal Baxter TQ-relations for open boundary quantum integrable systems
• Baxter operators for the quantum sl(3) invariant spin chain
• Gustafson integrals for $SL(2,\mathbb{C})$ spin magnet
• Non-intersection exponents of fully packed trails on the square lattice
• Separation of variables for symplectic characters
• Extended systems of Baxter Q-functions and fused flags I: simply-laced case
• Spin Chains and Gustafson's Integrals
• All correlation functions of the open XXX spin 1/2 quantum chains for unparallel boundary magnetic fields with one constraint
• Supersymmetric quantum mechanics of the flux tube
• Separation of Variables for a flux tube with an end
• Completeness of SoV Representation for $\mathrm{SL}(2,\mathbb{R})$ Spin Chains
• On scalar products and form factors by Separation of Variables: the antiperiodic XXZ model
• Separation of variables for higher rank integrable models: review of recent progress
• Finite size lattice results for the two-boundary Temperley--Lieb loop model
• On correlation functions for the open XXZ chain with non-longitudinal boundary fields : the case with a constraint
• Unitarity of the SoV Transform for $\mathrm{SL}(2,\mathbb{C})$ Spin Chains
• BC-type open $SL(2,\mathbb{C})$ spin chain
• The open XYZ spin 1/2 chain: Separation of Variables and scalar products for boundary fields related by a constraint