Scalar products of the open XYZ chain with non-diagonal boundary terms

Abstract

With the help of the F-basis provided by the Drinfeld twist or factorizing F-matrix of the eight-vertex solid-on-solid (SOS) model, we obtain the determinant representations of the scalar products of Bethe states for the open XYZ chain with non-diagonal boundary terms. By taking the on shell limit, we obtain the determinant representations (or Gaudin formula) of the norms of the Bethe states.

arXiv commentLatex file, 28 pages

References in corpus (54)

• Quantum Inverse Scattering Method and Correlation Functions
• Form factors of the XXZ Heisenberg spin-1/2 finite chain
• Bethe Ansatz Solution of the Asymmetric Exclusion Process with Open Boundaries
• Diagonalization of the XXZ Hamiltonian by Vertex Operators
• Bethe Ansatz solution of the open XXZ chain with nondiagonal boundary terms
• Exact Spectral Gaps of the Asymmetric Exclusion Process with Open Boundaries
• Functional relations and Bethe Ansatz for the XXZ chain
• Exact spectrum of the XXZ open spin chain from the q-Onsager algebra representation theory
• Functional relations from the Yang-Baxter algebra: Eigenvalues of the XXZ model with non-diagonal twisted and open boundary conditions
• Completeness of the Bethe Ansatz solution of the open XXZ chain with nondiagonal boundary terms
• Integrable XYZ Spin Chain with Boundaries
• Correlation functions of the open XXZ chain I
• Algebraic Bethe ansatz for the elliptic quantum group $E_{\tau ,\eta }(s{l}_2)$
• Determinant formula for the six-vertex model with reflecting end
• Q-operator and T-Q relation from the fusion hierarchy
• Magic in the spectra of the XXZ quantum chain with boundaries at Delta=0 and Delta=-1/2
• Bethe ansatz for the XXX-S chain with non-diagonal open boundaries
• Algebraic Bethe ansatz for eight vertex model with general open-boundary conditions
• Separation of variables for integrable spin-boson models
• Exact solution of the XXZ Gaudin model with generic open boundaries
• $T$-$Q$ relation and exact solution for the XYZ chain with general nondiagonal boundary terms
• Solution of the SU(N) Vertex Model with Non-Diagonal Open Boundaries
• Exact solution of the open XXZ chain with general integrable boundary terms at roots of unity
• On the second reference state and complete eigenstates of the open XXZ chain
• Staggered Polarization of Vertex Models with $U_q(\widehat{sl}(n))$-Symmetry
• Equivalences between spin models induced by defects
• $A_{n-1}$ Gaudin model with open boundaries
• Solution of the dual reflection equation for $A_{n-1}^{(1)}$ SOS model
• Spin Chains with Non-Diagonal Boundaries and Trigonometric SOS Model with Reflecting End
• Exact solution of $Z_n$ Belavin model with open boundary condition
• Exact solution of the $A_{n-1}^{(1)}$ trigonometric vertex model with non-diagonal open boundaries
• Bethe ansatz of the open spin-s XXZ chain with nondiagonal boundary terms
• Elliptic dynamical reflection algebra and partition function of SOS model with reflecting end
• The open XXZ and associated models at q root of unity
• Determinant Representations of Correlation Functions for the Supersymmetric t-J Model
• $Z_n$ elliptic Gaudin model with open boundaries
• Non-diagonal solutions of the reflection equation for the trigonometric $A_{n-1}^{(1)}$ vertex model
• Drinfeld Twists and Algebraic Bethe Ansatz of the Supersymmetric t-J Model
• On quantum group symmetry and Bethe ansatz for the asymmetric twin spin chain with integrable boundary
• The twisted quantum affine algebra $U_q(A^{(2)_2)$ and correlation functions of the Izergin-Korepin model
• Drinfeld twists and algebraic Bethe ansatz of the supersymmetric model associated with $U_q(gl(m|n))$
• Algebraic Bethe ansatz for the elliptic quantum group $E_{\tau ,\eta }(s{l}_n)$ and its applications
• Highest weight representations of $U_q(\widehat{sl}(2|1))$ and correlation functions of the q-deformed supersymmetric t-J model
• Multiple reference states and complete spectrum of the $Z_n$ Belavin model with open boundaries
• Drinfeld Twists and Symmetric Bethe Vectors of Supersymmetric Fermion Models
• Bosonization of quantum sine-Gordon field with a boundary
• Domain wall partition function of the eight-vertex model with a non-diagonal reflecting end
• Eigenvalues of Ruijsenaars-Schneider models associated with $A_{n-1}$ root system in Bethe ansatz formalism
• Determinant representations of scalar products for the open XXZ chain with non-diagonal boundary terms
• Partition function of the trigonometric SOS model with reflecting end
• Drinfeld twists of the open XXZ chain with non-diagonal boundary terms
• Determinant formula for the partition function of the six-vertex model with a non-diagonal reflecting end
• On the Construction of Correlation Functions for the Integrable Supersymmetric Fermion Models
• Level-one Highest Weight Representation of $U_q[\widehat{sl(N|1)}]$ and Bosonization of the Multi-component Super t-J Model

Cited by in corpus (10)

• Symmetric functions and wavefunctions of the six-vertex model by Izergin-Korepin analysis
• Thermodynamic limit of the spin-$\frac{1}{2}$ XYZ spin chain with the antiperiodic boundary condition
• Elliptic supersymmetric integrable model and multivariable elliptic functions
• Quantum inverse scattering method and generalizations of symplectic Schur functions and Whittaker functions
• Higher rank elliptic partition functions and multisymmetric elliptic functions
• Bethe/Gauge Correspondence for $A_N$ Spin Chains with Integrable Boundaries
• A class of partition functions associated with $E_{\tau ,\eta }(g{l}_3)$ by Izergin-Korepin analysis
• Scalar products of the elliptic Felderhof model and elliptic Cauchy formula
• Drinfeld twist and symmetric Bethe vectors of the open XYZ chain with non-diagonal boundary terms
• Elliptic free-fermion model with OS boundary and elliptic Pfaffians