Solving the open XXZ spin chain with nondiagonal boundary terms at roots of unity

Abstract

We consider the open XXZ quantum spin chain with nondiagonal boundary terms. For bulk anisotropy value η= i π/(p+1), p= 1, 2, ..., we propose an exact (p+1)-order functional relation for the transfer matrix, which implies Bethe-Ansatz-like equations for the corresponding eigenvalues. The key observation is that the fused spin-(p+1)/2 transfer matrix can be expressed in terms of a lower-spin transfer matrix, resulting in the truncation of the fusion hierarchy.

20 pages, LaTeX; amssymb, no figures; V3 contains Note Added giving coefficients c_{p,l}

References in corpus (1)

• Bethe Ansatz solution of the open XX spin chain with nondiagonal boundary terms

Cited by in corpus (86)

• 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
• Exact spectrum of the XXZ open spin chain from the q-Onsager algebra representation theory
• Antiperiodic spin-1/2 XXZ quantum chains by separation of variables: Complete spectrum and form factors
• 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
• Completeness of the Bethe Ansatz solution of the open XXZ chain with nondiagonal boundary terms
• Off-diagonal Bethe ansatz solution of the XXX spin-chain with arbitrary boundary conditions
• Quantizing Open Spin Chains with Variable Length: an example from Giant Gravitons
• Q-operator and T-Q relation from the fusion hierarchy
• 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
• From the Quantum Transfer Matrix to the Quench Action: The Loschmidt echo in $XXZ$ Heisenberg spin chains
• The q-deformed analogue of the Onsager algebra: Beyond the Bethe ansatz approach
• Non-analytic behavior of the Loschmidt echo in XXZ spin chains: exact results
• Integrable approach to simple exclusion processes with boundaries. Review and progress
• A deformed analogue of Onsager's symmetry in the XXZ open spin chain
• 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
• Thermodynamic limit and surface energy of the XXZ spin chain with arbitrary boundary fields
• $T$-$Q$ relation and exact solution for the XYZ chain with general nondiagonal boundary terms
• Bethe Ansatz for the Temperley-Lieb loop model with open boundaries
• Exact solution of the open XXZ chain with general integrable boundary terms at roots of unity
• Functional Bethe ansatz methods for the open XXX chain
• Bethe states of the XXZ spin-1/2 chain with arbitrary boundary fields
• Sine-Gordon quantum field theory on the half-line with quantum boundary degrees of freedom
• Open spin chains with generic integrable boundaries: Baxter equation and Bethe ansatz completeness from SOV
• Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra I
• Bethe Ansatz derived from the functional relations of the open XXZ chain for new special cases
• The XXZ model with anti-periodic twisted boundary conditions
• 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
• Exact solution of the $A_{n-1}^{(1)}$ trigonometric vertex model with non-diagonal open boundaries
• Nested Bethe ansatz for `all' open spin chains with diagonal boundary conditions
• Bethe ansatz of the open spin-s XXZ chain with nondiagonal boundary terms
• Solutions of the boundary Yang-Baxter equation for arbitrary spin
• The open XXZ spin chain in the SoV framework: scalar product of separate states
• Integrable quenches in nested spin chains II: fusion of boundary transfer matrices
• Scale-free non-Hermitian skin effect in a boundary-dissipated spin chain
• Exact surface energy and helical spinons in the XXZ spin chain with arbitrary non-diagonal boundary fields
• Exact ground state and elementary excitations of a topological spin chain
• Algebraic Bethe ansatz for the six vertex model with upper triangular $K$-matrices
• Fusion Operators in the Generalized ${\tau }^{(2)}$-model and Root-of-unity Symmetry of the XXZ Spin Chain of Higher Spin
• Exact solution of the spin-s Heisenberg chain with generic non-diagonal boundaries
• Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra II
• Exact boundary free energy of the open XXZ chain with arbitrary boundary conditions
• Exact solution of the XXX Gaudin model with the generic open boundaries
• The Q-operator for Root-of-Unity Symmetry in Six Vertex Model
• On Separation of Variables for Reflection Algebras
• Nested Bethe ansatz for Y(gl(n)) open spin chains with diagonal boundary conditions
• Generalized T-Q relations and the open XXZ chain
• Off-diagonal Bethe Ansatz on the $so(5)$ spin chain
• Entanglement and boundary entropy in quantum spin chains with arbitrary direction of the boundary magnetic fields
• Correlation functions for open XXZ spin 1/2 quantum chains with unparallel boundary magnetic fields
• Inversion identities for inhomogeneous face models
• Entanglement entropy in quantum spin chains with broken parity number symmetry
• Truncation identities for the small polaron fusion hierarchy
• Bethe Ansatz solution of the small polaron with nondiagonal boundary terms
• All correlation functions of the open XXX spin 1/2 quantum chains for unparallel boundary magnetic fields with one constraint
• Generalized T-Q relations and the open spin-s XXZ chain with nondiagonal boundary terms
• Extended T-systems, Q matrices and T-Q relations for $s\ell (2)$ models at roots of unity
• Exact ground state and elementary excitations of a competing spin chain with twisted boundary condition
• On the complete-spectrum characterization of quantum integrable spin chains via the inhomogeneous T-Q relation
• Exact solution of the $sp(4)$ integrable spin chain with generic boundaries
• A representation basis for the quantum integrable spin chain associated with the su(3) algebra
• Exact solution of the quantum integrable model associated with the twisted $D_3^{(2)}$ algebra
• The solution of an open XXZ chain with arbitrary spin revisited
• Bethe ansatz solution of the ${\tau }_2$-model with arbitrary boundary fields
• Finite-size correction and bulk hole-excitations for special case of an open XXZ chain with nondiagonal boundary terms at roots of unity
• Spin Drude weight for the integrable XXZ chain with arbitrary spin
• 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
• On correlation functions for the open XXZ chain with non-longitudinal boundary fields : the case with a constraint
• 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
• Functional Equations and Fusion Matrices for the Eight Vertex Model
• The spectrum of an open vertex model based on the U_q[SU(2)] at roots of unity
• Fermionic reflection matrices
• Mapping current and activity fluctuations in exclusion processes: consequences and open questions
• Graded Off-diagonal Bethe ansatz solution of the $SU(2|2)$ spin chain model with generic integrable boundaries
• Bethe Ansatz and boundary energy of the open spin-1/2 XXZ chain