Modified algebraic Bethe ansatz for XXZ chain on the segment - II - general cases

Abstract

The spectral problem of the Heisenberg XXZ spin-$\frac{1}{2}$ chain on the segment is investigated within a modified algebraic Bethe ansatz framework. We consider in this work the most general boundaries allowed by integrability. The eigenvalues and the eigenvectors are obtained. They are characterised by a set of Bethe roots with cardinality equal to $N$, the length of the chain, and which satisfies a set of Bethe equations with an additional term.

arXiv commentV2 published version

References in corpus (31)

• Form factors of the XXZ Heisenberg spin-1/2 finite chain
• 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
• Exact spectrum of the XXZ open spin chain from the q-Onsager algebra representation theory
• Off-diagonal Bethe ansatz solutions of the anisotropic spin-1/2 chains with arbitrary boundary fields
• Functional relations from the Yang-Baxter algebra: Eigenvalues of the XXZ model with non-diagonal twisted and open boundary conditions
• Solving the open XXZ spin chain with nondiagonal boundary terms at roots of unity
• Completeness of the Bethe Ansatz solution of the open XXZ chain with nondiagonal boundary terms
• The half-infinite XXZ chain in Onsager's approach
• Correlation functions of the open XXZ chain I
• Non-diagonal open spin-1/2 XXZ quantum chains by separation of variables: Complete spectrum and matrix elements of some quasi-local operators
• Heisenberg XXX Model with General Boundaries: Eigenvectors from Algebraic Bethe Ansatz
• 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
• Correlation functions of the open XXZ chain II
• Eigenvectors of open XXZ and ASEP models for a class of non-diagonal boundary conditions
• Algebraic Bethe ansatz for open XXX model with triangular boundary matrices
• Matrix Coordinate Bethe Ansatz: Applications to XXZ and ASEP models
• Thermodynamic limit and surface energy of the XXZ spin chain with arbitrary boundary fields
• Bethe Ansatz for the Temperley-Lieb loop model with open boundaries
• Bethe states of the XXZ spin-1/2 chain with arbitrary boundary fields
• On the second reference state and complete eigenstates of the open XXZ chain
• Open spin chains with generic integrable boundaries: Baxter equation and Bethe ansatz completeness from SOV
• Exact solutions and elementary excitations in the XXZ spin chain with unparallel boundary fields
• Bethe Ansatz and Q-operator for the open ASEP
• Spin Chains with Non-Diagonal Boundaries and Trigonometric SOS Model with Reflecting End
• Algebraic Bethe ansatz for the six vertex model with upper triangular $K$-matrices
• Determinant formula for the partition function of the six-vertex model with a non-diagonal reflecting end
• Algebraic Bethe ansatz for 19-vertex models with upper triangular K-matrices

Cited by in corpus (58)

• The Physicist's Companion to Current Fluctuations: One-Dimensional Bulk-Driven Lattice Gases
• Modified algebraic Bethe ansatz for XXZ chain on the segment - I - triangular cases
• Modified algebraic Bethe ansatz for XXZ chain on the segment - III - Proof
• The open XXX spin chain in the SoV framework: scalar product of separate states
• Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra I
• Complete spectrum of quantum integrable lattice models associated to Y(gl(n)) by separation of variables
• Slavnov and Gaudin-Korepin Formulas for Models without $\mathrm{U}(1)$ Symmetry: the Twisted XXX Chain
• Why scalar products in the algebraic Bethe ansatz have determinant representation
• Scale-free non-Hermitian skin effect in a boundary-dissipated spin chain
• Phantom Bethe roots in the integrable open spin $1/2$ $XXZ$ chain
• The open XXZ spin chain in the SoV framework: scalar product of separate states
• Modified Algebraic Bethe Ansatz: Twisted XXX Case
• Algebraic Bethe Ansatz for the XXZ Gaudin Models with Generic Boundary
• Diagonalization of the Heun-Askey-Wilson operator, Leonard pairs and the algebraic Bethe ansatz
• Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra II
• Chiral coordinate Bethe ansatz for phantom eigenstates in the open XXZ spin-$\frac{1}{2}$ chain
• Heun operator of Lie type and the modified algebraic Bethe ansatz
• Scalar product of twisted XXX modified Bethe vectors
• On Separation of Variables for Reflection Algebras
• Scalar Products in Twisted XXX Spin Chain. Determinant Representation
• Algebraic Bethe ansatz for the XXZ Heisenberg spin chain with triangular boundaries and the corresponding Gaudin model
• A note on ${\mathfrak{gl}}_2$-invariant Bethe vectors
• Equivalent T-Q relations and exact results for the open TASEP
• Slavnov and Gaudin-Korepin formulas for models without $U(1)$ symmetry: the XXX chain on the segment
• The Heun-Racah and Heun-Bannai-Ito algebras
• Off-diagonal Bethe Ansatz on the $so(5)$ spin chain
• 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
• Scalar product for the XXZ spin chain with general integrable boundaries
• Exact solution of an su(n) spin torus
• All correlation functions of the open XXX spin 1/2 quantum chains for unparallel boundary magnetic fields with one constraint
• Exact solutions of the $C_n$ quantum spin chain
• $U_q{\mathfrak{sl}}_2$-invariant non-compact boundary conditions for the XXZ spin chain
• Exact solution of the $sp(4)$ integrable spin chain with generic boundaries
• Off-diagonal Bethe Ansatz for the $D_3^{(1)}$ model
• Exact ground state and elementary excitations of a competing spin chain with twisted boundary condition
• Bethe ansatz diagonalization of the Heun-Racah operator
• The rational Sklyanin algebra and the Wilson and para-Racah polynomials
• Algebraic Bethe ansatz for the Temperley-Lieb spin-1 chain
• 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
• Exact solution of the quantum integrable model associated with the twisted $D_3^{(2)}$ algebra
• Bethe states of the trigonometric SU(3) spin chain with generic open boundaries
• On scalar products and form factors by Separation of Variables: the antiperiodic XXZ model
• Elementary excitations in an integrable twisted J1-J2 spin chain in the thermodynamic limit
• Exact solution of the trigonometric SU(3) spin chain with generic off-diagonal boundary reflections
• Time and band limiting operator and Bethe ansatz
• On correlation functions for the open XXZ chain with non-longitudinal boundary fields : the case with a constraint
• Surface energy and elementary excitations of the XYZ spin chain with integrable open boundary fields
• Off-diagonal approach to the exact solution of quantum integrable systems
• Root patterns and exact surface energy of the spin-1 Heisenberg model with generic open boundaries
• Non-linear integral equations for the XXX spin-1/2 quantum chain with non-diagonal boundary fields
• Universal TT- and TQ-relations via centrally extended q-Onsager algebra
• Spectrum of the transfer matrices of the spin chains associated with the $A_3^{(2)}$ Lie algebra
• Bethe States of the integrable spin-s chain with generic open boundaries
• "Bethe-Ansatz-free" eigenstates of spin-1/2 Richardson-Gaudin integrable models
• Graded Off-diagonal Bethe ansatz solution of the $SU(2|2)$ spin chain model with generic integrable boundaries
• On the ${\mathcal{U}}_q[osp(1|2)]$ Temperley-Lieb model