Inhomogeneous T-Q equation for the open XXX chain with general boundary terms: completeness and arbitrary spin

Abstract

An inhomogeneous T-Q equation has recently been proposed by Cao, Yang, Shi and Wang for the open spin-1/2 XXX chain with general (nondiagonal) boundary terms. We argue that a simplified version of this equation describes all the eigenvalues of the transfer matrix of this model. We also propose a generating function for the inhomogeneous T-Q equations of arbitrary spin.

8 pages; v2: minor improvements

References in corpus (5)

• Off-diagonal Bethe ansatz and exact solution of a topological spin ring
• Off-diagonal Bethe ansatz solutions of the anisotropic spin-1/2 chains with arbitrary boundary fields
• Off-diagonal Bethe ansatz solution of the XXX spin-chain with arbitrary boundary conditions
• Spin-1/2 XYZ model revisit: general solutions via off-diagonal Bethe ansatz
• The spectrum of tachyons in AdS/CFT

Cited by in corpus (38)

• Heisenberg XXX Model with General Boundaries: Eigenvectors from Algebraic Bethe Ansatz
• Modified algebraic Bethe ansatz for XXZ chain on the segment - I - triangular cases
• Dynamical free energy and the Loschmidt-echo for a class of quantum quenches in the Heisenberg spin chain
• From the Quantum Transfer Matrix to the Quench Action: The Loschmidt echo in $XXZ$ Heisenberg spin chains
• Non-analytic behavior of the Loschmidt echo in XXZ spin chains: exact results
• Integrable approach to simple exclusion processes with boundaries. Review and progress
• The open XXX spin chain in the SoV framework: scalar product of separate states
• Thermodynamic limit and surface energy of the XXZ spin chain with arbitrary boundary fields
• Bethe states of the XXZ spin-1/2 chain with arbitrary boundary fields
• Exact solution of the one-dimensional Hubbard model with arbitrary boundary magnetic fields
• Exact solution of the Izergin-Korepin model with general non-diagonal boundary terms
• Thermodynamic limit and boundary energy of the SU(3) spin chain with non-diagonal boundary fields
• Modified Algebraic Bethe Ansatz: Twisted XXX Case
• Algebraic Bethe Ansatz for the XXZ Gaudin Models with Generic Boundary
• Bethe ansatz for an AdS/CFT open spin chain with non-diagonal boundaries
• Scalar Products in Twisted XXX Spin Chain. Determinant Representation
• Equivalent T-Q relations and exact results for the open TASEP
• 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
• Thermodynamic limit and twisted boundary energy of the XXZ spin chain with antiperiodic boundary condition
• Root patterns and energy spectra of quantum integrable systems without $U(1)$ symmetry: antiperiodic $XXZ$ spin chain
• Scalar product for the XXZ spin chain with general integrable boundaries
• Inversion identities for inhomogeneous face models
• Thermodynamic limit and boundary energy of the spin-1 Heisenberg chain with non-diagonal boundary fields
• Exact solution of the $sp(4)$ integrable spin chain with generic boundaries
• Off-diagonal Bethe Ansatz for the $D_3^{(1)}$ model
• Wronskian-type formula for inhomogeneous TQ-equations
• Thermodynamic limit of the spin-$\frac{1}{2}$ XYZ spin chain with the antiperiodic boundary condition
• Bethe ansatz diagonalization of the Heun-Racah operator
• An inhomogeneous Lax representation for the Hirota equation
• Exact Spin Correlators of Integrable Quantum Circuits from Algebraic Geometry
• Algebraic Bethe ansatz for 19-vertex models with upper triangular K-matrices
• Time and band limiting operator and Bethe ansatz
• Exact solution of the trigonometric SU(3) spin chain with generic off-diagonal boundary reflections
• Inhomogeneous discrete-time exclusion processes
• Non-linear integral equations for the XXX spin-1/2 quantum chain with non-diagonal boundary fields
• Bethe/Gauge Correspondence for $A_N$ Spin Chains with Integrable Boundaries
• Exact physical quantities of a competing spin chain in the thermodynamic limit