Off-diagonal Bethe ansatz solution of the XXX spin-chain with arbitrary boundary conditions

Abstract

With the off-diagonal Bethe ansatz method proposed recently by the present authors, we exactly diagonalize the $XXX$ spin chain with arbitrary boundary fields. By constructing a functional relation between the eigenvalues of the transfer matrix and the quantum determinant, the associated $T-Q$ relation and the Bethe ansatz equations are derived.

19 pages, published version

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• Integrable approach to simple exclusion processes with boundaries. Review and progress
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• An integrable case of the p+ip pairing Hamiltonian interacting with its environment
• Thermodynamic limit and boundary energy of the SU(3) spin chain with non-diagonal boundary fields
• Integrable quenches in nested spin chains II: fusion of boundary transfer matrices
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• Exact solution of the one-dimensional super-symmetric t-J model with unparallel boundary fields
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• Modified Algebraic Bethe Ansatz: Twisted XXX Case
• Algebraic geometry and Bethe ansatz (I) the quotient ring for BAE
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• Algebraic Bethe ansatz for the XXX chain with triangular boundaries and Gaudin model
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• Exact solution of the XXX Gaudin model with the generic open boundaries
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• Exact boundary free energy of the open XXZ chain with arbitrary boundary conditions
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• Algebraic Bethe ansatz for the sl(2) Gaudin model with boundary
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• 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
• Super-Spin Chains for 6D SCFTs
• Boundary energy of the open XXX chain with a non-diagonal boundary term
• Thermodynamic limit and twisted boundary energy of the XXZ spin chain with antiperiodic boundary condition
• Entanglement entropy in quantum spin chains with broken parity number symmetry
• Inversion identities for inhomogeneous face models
• Exact solution of an su(n) spin torus
• Non-Abelian $SU(3{)}_k$ anyons: inversion identities for higher rank face models
• Shor-Movassagh chain leads to unusual integrable model
• $T$-$Q$ relations for the integrable two-species asymmetric simple exclusion process with open boundaries
• Surface energy and elementary excitations of the XXZ spin chain with arbitrary boundary fields
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• Wronskian-type formula for inhomogeneous TQ-equations
• Exact surface energy of the $D_2^{(1)}$ spin chain with generic non-diagonal boundary reflections
• An inhomogeneous Lax representation for the Hirota equation
• A representation basis for the quantum integrable spin chain associated with the su(3) algebra
• Bethe states of the trigonometric SU(3) spin chain with generic open boundaries
• Geometry of Massless Scattering in Integrable Superstring
• Exact solution of the quantum integrable model associated with the twisted $D_3^{(2)}$ algebra
• Exact solution of the trigonometric SU(3) spin chain with generic off-diagonal boundary reflections
• A study of integrable form factors in massless relativistic $Ad{S}_2$
• Bethe States of the integrable spin-s chain with generic open boundaries
• Spectrum-preserving deformations of integrable spin chains with open boundaries
• Small polaron with generic open boundary conditions revisit: exact solution via the off-diagonal Bethe ansatz
• Exact solution of the Izergin-Korepin Gaudin model with periodic and open boundaries
• Canonical formulation for the thermodynamics of $s{l}_n$-invariant integrable spin chains
• On the solutions of the $Z_n$-Belavin model with arbitrary number of sites