Bethe states of the XXZ spin-1/2 chain with arbitrary boundary fields

Abstract

Based on the inhomogeneous T-Q relation constructed via the off-diagonal Bethe Ansatz, the Bethe-type eigenstates of the XXZ spin-1/2 chain with arbitrary boundary fields are constructed. It is found that by employing two sets of gauge transformations, proper generators and reference state for constructing Bethe vectors can be obtained respectively. Given an inhomogeneous T-Q relation for an eigenvalue, it is proven that the resulting Bethe state is an eigenstate of the transfer matrix, provided that the parameters of the generators satisfy the associated Bethe Ansatz equations.

arXiv comment24 pages, no figure, published version

References in corpus (34)

• Review of AdS/CFT Integrability: An Overview
• Boundary S-Matrix and Boundary State in Two-Dimensional Integrable Quantum Field Theory
• Separation of Variables. New Trends.
• Bethe Ansatz Solution of the Asymmetric Exclusion Process with Open Boundaries
• Diffusion and ballistic transport in one-dimensional quantum systems
• Boundary K-Matrices for the Six Vertex and the n(2n-1) A_{n-1} Vertex Models
• Bethe Ansatz solution of the open XXZ chain with nondiagonal boundary terms
• Off-diagonal Bethe ansatz and exact solution of a topological spin ring
• Functional relations and Bethe Ansatz for the XXZ chain
• Off-diagonal Bethe ansatz solutions of the anisotropic spin-1/2 chains with arbitrary boundary fields
• Solving the open XXZ spin chain with nondiagonal boundary terms at roots of unity
• Functional relations from the Yang-Baxter algebra: Eigenvalues of the XXZ model with non-diagonal twisted and open boundary conditions
• The half-infinite XXZ chain in Onsager's approach
• Off-diagonal Bethe ansatz solution of the XXX spin-chain with arbitrary boundary conditions
• Non-diagonal open spin-1/2 XXZ quantum chains by separation of variables: Complete spectrum and matrix elements of some quasi-local operators
• Q-operator and T-Q relation from the fusion hierarchy
• Modified algebraic Bethe ansatz for XXZ chain on the segment - I - triangular cases
• Magic in the spectra of the XXZ quantum chain with boundaries at Delta=0 and Delta=-1/2
• Complete spectrum and scalar products for the open spin-1/2 XXZ quantum chains with non-diagonal boundary terms
• The q-deformed analogue of the Onsager algebra: Beyond the Bethe ansatz approach
• Algebraic Bethe ansatz for eight vertex model with general open-boundary conditions
• Exact solution of the XXZ Gaudin model with generic open boundaries
• Spin-1/2 XYZ model revisit: general solutions via off-diagonal Bethe ansatz
• Algebraic Bethe ansatz for open XXX model with triangular boundary matrices
• Thermodynamic limit and surface energy of the XXZ spin chain with arbitrary boundary fields
• Inhomogeneous T-Q equation for the open XXX chain with general boundary terms: completeness and arbitrary spin
• Open spin chains with generic integrable boundaries: Baxter equation and Bethe ansatz completeness from SOV
• Solution of the dual reflection equation for $A_{n-1}^{(1)}$ SOS model
• Nested off-diagonal Bethe ansatz and exact solutions of the su(n) spin chain with generic integrable boundaries
• Bethe Ansatz solution of the open XX spin chain with nondiagonal boundary terms
• Exact solution of $Z_n$ Belavin model with open boundary condition
• Exact solution of the Izergin-Korepin model with general non-diagonal boundary terms
• Exact solution of the spin-s Heisenberg chain with generic non-diagonal boundaries
• Exact solution of the XXZ alternating spin chain with generic non-diagonal boundaries

Cited by in corpus (29)

• Modified algebraic Bethe ansatz for XXZ chain on the segment - II - general cases
• Modified algebraic Bethe ansatz for XXZ chain on the segment - III - Proof
• Phantom Bethe excitations and spin helix eigenstates in integrable periodic and open spin chains
• Phantom Bethe roots in the integrable open spin $1/2$ $XXZ$ chain
• Quantum impurity in a Luttinger liquid: Exact solution of the Kane-Fisher model
• Modified Algebraic Bethe Ansatz: Twisted XXX Case
• Exact surface energy and helical spinons in the XXZ spin chain with arbitrary non-diagonal boundary fields
• Chiral coordinate Bethe ansatz for phantom eigenstates in the open XXZ spin-$\frac{1}{2}$ chain
• Scalar product of twisted XXX modified Bethe vectors
• Common framework and quadratic Bethe equations for rational Gaudin magnets in arbitrarily oriented magnetic fields
• Equivalent T-Q relations and exact results for the open TASEP
• Algebraic Bethe ansatz for the XXZ Heisenberg spin chain with triangular boundaries and the corresponding Gaudin model
• Slavnov and Gaudin-Korepin formulas for models without $U(1)$ symmetry: the XXX chain on the segment
• Scalar product for the XXZ spin chain with general integrable boundaries
• Boundary versus bulk behavior of time-dependent correlation functions in one-dimensional quantum systems
• Spectrum of the quantum integrable $D_2^{(2)}$ spin chain with generic boundary fields
• Surface energy and elementary excitations of the XXZ spin chain with arbitrary boundary fields
• A Pedestrian's Way to Baxter's Bethe Ansatz for the Periodic XYZ Chain
• On the complete-spectrum characterization of quantum integrable spin chains via the inhomogeneous T-Q relation
• Exact surface energy of the $D_2^{(1)}$ spin chain with generic non-diagonal boundary reflections
• A representation basis for the quantum integrable spin chain associated with the su(3) algebra
• A bispectral q-hypergeometric basis for a class of quantum integrable models
• Bethe states of the trigonometric SU(3) spin chain with generic open boundaries
• Bethe States of the integrable spin-s chain with generic open boundaries
• Bethe/Gauge Correspondence for $A_N$ Spin Chains with Integrable Boundaries
• Spectrum-preserving deformations of integrable spin chains with open boundaries
• Scattering matrix of elementary excitations in the antiperiodic XXZ spin chain with η=iπ/3
• T-W relation and free energy of the antiperiodic XXZ chain with η=iπ/3 at a finite temperature
• A note on a boundary sine-Gordon model at the free-Fermion point