Functional relations from the Yang-Baxter algebra: Eigenvalues of the XXZ model with non-diagonal twisted and open boundary conditions

Abstract

In this work we consider a functional method in the theory of exactly solvable models based on the Yang-Baxter algebra. Using this method we derive the eigenvalues of the XXZ model with non-diagonal twisted and open boundary conditions for general values of the anisotropy and boundary parameters.

26 pages

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• Bethe ansatz for the XXX-S chain with non-diagonal open boundaries
• Few remarks on Baecklund transformations for many-body systems
• Exact solution for the spin-$s$ XXZ quantum chain with non-diagonal twists
• Algebraic Bethe ansatz for eight vertex model with general open-boundary conditions
• Solution of the SU(N) Vertex Model with Non-Diagonal Open Boundaries
• $T$-$Q$ relation and exact solution for the XYZ chain with general nondiagonal boundary terms
• 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
• Bethe Ansatz derived from the functional relations of the open XXZ chain for new special cases
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• Spectrum of the supersymmetric t-J model with non-diagonal open boundaries
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Cited by in corpus (83)

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• The half-infinite XXZ chain in Onsager's approach
• Off-diagonal Bethe ansatz solution of the XXX spin-chain with arbitrary boundary conditions
• Construction of a Coordinate Bethe Ansatz for the asymmetric simple exclusion process with open boundaries
• Non-diagonal open spin-1/2 XXZ quantum chains by separation of variables: Complete spectrum and matrix elements of some quasi-local operators
• Separation of Variables in the open XXX chain
• Heisenberg XXX Model with General Boundaries: Eigenvectors from Algebraic Bethe Ansatz
• Modified algebraic Bethe ansatz for XXZ chain on the segment - I - triangular cases
• Modified algebraic Bethe ansatz for XXZ chain on the segment - II - general cases
• Complete spectrum and scalar products for the open spin-1/2 XXZ quantum chains with non-diagonal boundary terms
• Modified algebraic Bethe ansatz for XXZ chain on the segment - III - Proof
• Integrable approach to simple exclusion processes with boundaries. Review and progress
• Separation of variables for integrable spin-boson models
• Eigenvectors of open XXZ and ASEP models for a class of non-diagonal boundary conditions
• The open XXX spin chain in the SoV framework: scalar product of separate states
• Matrix Coordinate Bethe Ansatz: Applications to XXZ and ASEP models
• Antiperiodic dynamical 6-vertex model I: Complete spectrum by SOV, matrix elements of the identity on separate states and connections to the periodic 8-vertex model
• Functional Bethe ansatz methods for the open XXX chain
• Bethe states of the XXZ spin-1/2 chain with arbitrary boundary fields
• Open spin chains with generic integrable boundaries: Baxter equation and Bethe ansatz completeness from SOV
• Form factors and complete spectrum of XXX antiperiodic higher spin chains by quantum separation of variables
• Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra I
• The XXZ model with anti-periodic twisted boundary conditions
• Slavnov and Gaudin-Korepin Formulas for Models without $\mathrm{U}(1)$ Symmetry: the Twisted XXX Chain
• Nested off-diagonal Bethe ansatz and exact solutions of the su(n) spin chain with generic integrable boundaries
• Exact solution of the Izergin-Korepin model with general non-diagonal boundary terms
• Functional relations for the six vertex model with domain wall boundary conditions
• Bethe ansatz of the open spin-s XXZ chain with nondiagonal boundary terms
• Fluctuations and skewness of the current in the partially asymmetric exclusion process
• On the boundaries of quantum integrability for the spin-1/2 Richardson-Gaudin system
• Correlation functions of the half-infinite XXZ spin chain with a triangular boundary
• The open XXZ spin chain in the SoV framework: scalar product of separate states
• Algebraic Bethe Ansatz for the XXZ Gaudin Models with Generic Boundary
• Algebraic Bethe ansatz for the six vertex model with upper triangular $K$-matrices
• Exact ground state and elementary excitations of a topological spin chain
• Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra II
• Exact solution of the spin-s Heisenberg chain with generic non-diagonal boundaries
• Algebraic Bethe ansatz for the totally asymmetric simple exclusion process with boundaries
• Reflection algebra and functional equations
• Non-diagonal boundary conditions for gl(1|1) super spin chains
• Common framework and quadratic Bethe equations for rational Gaudin magnets in arbitrarily oriented magnetic fields
• Domain wall partition function of the eight-vertex model with a non-diagonal reflecting end
• On Separation of Variables for Reflection Algebras
• Slavnov and Gaudin-Korepin formulas for models without $U(1)$ symmetry: the XXX chain on the segment
• Off-diagonal Bethe Ansatz on the $so(5)$ spin chain
• Scalar products of the open XYZ chain with non-diagonal boundary terms
• Determinant representations of scalar products for the open XXZ chain with non-diagonal boundary terms
• Reflection matrices for the $U_q[sl(m|n{)}^{(1)}]$ vertex model
• Off-shell scalar products for the $XXZ$ spin chain with open boundaries
• Form factors of the half-infinite XXZ spin chain with a triangular boundary
• Drinfeld twists of the open XXZ chain with non-diagonal boundary terms
• Twisted Heisenberg chain and the six-vertex model with DWBC
• Integral formula for elliptic SOS models with domain walls and a reflecting end
• Inversion identities for inhomogeneous face models
• Functional relations and the Yang-Baxter algebra
• Determinant formula for the partition function of the six-vertex model with a non-diagonal reflecting end
• On the ${\mathcal{U}}_q[sl(2)]$ Temperley-Lieb reflection matrices
• Partial differential equations from integrable vertex models
• Bethe Ansatz solution of the small polaron with nondiagonal boundary terms
• Truncation identities for the small polaron fusion hierarchy
• New differential equations in the six-vertex model
• Generalized T-Q relations and the open spin-s XXZ chain with nondiagonal boundary terms
• Nested algebraic Bethe ansatz for open spin chains with even twisted Yangian symmetry
• Antiperiodic XXZ chains with arbitrary spins: Complete eigenstate construction by functional equations in separation of variables
• Differential approach to on-shell scalar products in six-vertex models
• A bispectral q-hypergeometric basis for a class of quantum integrable models
• The solution of an open XXZ chain with arbitrary spin revisited
• Scalar product of Bethe vectors from functional equations
• Six-vertex model and non-linear differential equations I. Spectral problem
• Generic boundary scattering in the open XXZ chain
• On the elliptic ${\mathfrak{gl}}_2$ solid-on-solid model: functional relations and determinants
• Continuous representations of scalar products of Bethe vectors
• A note on the IR limit of the NLIEs of boundary supersymmetric sine-Gordon model
• Domain-wall boundaries through non-diagonal twists in the six-vertex model
• Scattering matrix of elementary excitations in the antiperiodic XXZ spin chain with η=iπ/3
• Boundary S matrix of an open XXZ spin chain with nondiagonal boundary terms
• Drinfeld twist and symmetric Bethe vectors of the open XYZ chain with non-diagonal boundary terms
• Fermionic reflection matrices
• 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
• Six-vertex model and non-linear differential equations II. Continuous symmetries