Functional relations and Bethe Ansatz for the XXZ chain

Abstract

There is an approach due to Bazhanov and Reshetikhin for solving integrable RSOS models which consists of solving the functional relations which result from the truncation of the fusion hierarchy. We demonstrate that this is also an effective means of solving integrable vertex models. Indeed, we use this method to recover the known Bethe Ansatz solutions of both the closed and open XXZ quantum spin chains with U(1) symmetry. Moreover, since this method does not rely on the existence of a pseudovacuum state, we also use this method to solve a special case of the open XXZ chain with nondiagonal boundary terms.

13 pages, LaTeX; amssymb, amsmath, no figures

Cited by in corpus (101)

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• Bethe Ansatz solution of the open XXZ chain with nondiagonal boundary terms
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• 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
• 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
• 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
• Current large deviation function for the open asymmetric simple exclusion process
• 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
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• One-boundary Temperley-Lieb algebras in the XXZ and loop models
• The two-boundary Temperley-Lieb algebra
• Reconstruction of Baxter Q-operator from Sklyanin SOV for cyclic representations of integrable quantum models
• Matrix Coordinate Bethe Ansatz: Applications to XXZ and ASEP models
• Slowest relaxation mode of the partially asymmetric exclusion process with 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
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• On the second reference state and complete eigenstates of the open XXZ chain
• Bethe states of the XXZ spin-1/2 chain with arbitrary boundary fields
• Equivalences between spin models induced by defects
• Completeness of Bethe Ansatz by Sklyanin SOV for Cyclic Representations of Integrable Quantum Models
• Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra I
• The XXZ model with anti-periodic twisted boundary conditions
• Bethe Ansatz derived from the functional relations of the open XXZ chain for new special cases
• Baxter-Bazhanov-Stroganov model: Separation of Variables and Baxter Equation
• Bethe Ansatz and Q-operator for the open ASEP
• Classification of reflection matrices related to (super) Yangians and application to open spin chain models
• Analytic theory of the eight-vertex model
• Generalized coordinate Bethe ansatz for non diagonal boundaries
• $A_{n-1}$ Gaudin model with open boundaries
• Nested off-diagonal Bethe ansatz and exact solutions of the su(n) spin chain with generic integrable boundaries
• Complete Bethe Ansatz solution of the open spin-s XXZ chain with general integrable boundary terms
• Finite size effects in the XXZ and sine-Gordon models with two boundaries
• Exact solution of the Izergin-Korepin model with general non-diagonal boundary terms
• 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
• Exact solution of the $A_{n-1}^{(1)}$ trigonometric vertex model with non-diagonal open boundaries
• The open XXZ and associated models at q root of unity
• Dynamical Transition in the Open-boundary Totally Asymmetric Exclusion Process
• Excited states NLIE for sine-Gordon model in a strip with Dirichlet boundary conditions
• Phantom Bethe roots in the integrable open spin $1/2$ $XXZ$ chain
• Scale-free non-Hermitian skin effect in a boundary-dissipated spin chain
• NLIE for hole excited states in the sine-Gordon model with two boundaries
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• 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
• Finite size effects in the spin-1 XXZ and supersymmetric sine-Gordon models with Dirichlet boundary conditions
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• A note on the boundary spin $s$ XXZ chain
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• Auxiliary matrices for the six-vertex model and the algebraic Bethe ansatz
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• 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
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• Structure of the two-boundary XXZ model with non-diagonal boundary terms
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• Determinant formula for the partition function of the six-vertex model with a non-diagonal reflecting end
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• Inversion identities for inhomogeneous face models
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• $U_q{\mathfrak{sl}}_2$-invariant non-compact boundary conditions for the XXZ spin chain
• $T$-$Q$ relations for the integrable two-species asymmetric simple exclusion process with open boundaries
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• Coordinate Bethe Ansätze for non-diagonal boundaries
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• Extended T-systems, Q matrices and T-Q relations for $s\ell (2)$ models at roots of unity
• A representation basis for the quantum integrable spin chain associated with the su(3) algebra
• Finite-size correction and bulk hole-excitations for special case of an open XXZ chain with nondiagonal boundary terms at roots of unity
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• Algebraic Bethe Ansatz for the Open XXZ Spin Chain with Non-Diagonal Boundary Terms via $U_{\mathfrak{q}}{\mathfrak{sl}}_2$ Symmetry
• Generic boundary scattering in the open XXZ chain
• Exact solution of the trigonometric SU(3) spin chain with generic off-diagonal boundary reflections
• Theta function solutions of the qKZB equation for a face model
• Drinfeld twist and symmetric Bethe vectors of the open XYZ chain with non-diagonal boundary terms
• A note on the IR limit of the NLIEs of boundary supersymmetric sine-Gordon model
• Non-linear integral equations for the XXX spin-1/2 quantum chain with non-diagonal boundary fields
• On the NLIE of (inhomogeneous) open spin-1 XXZ chain with general integrable boundary terms
• Non-diagonal reflection for the non-critical XXZ model
• Bethe Ansatz and boundary energy of the open spin-1/2 XXZ chain
• NLIE and finite size effects of the spin-1/2 XXZ and sine-Gordon models with two boundaries revisited
• A note on a boundary sine-Gordon model at the free-Fermion point