Algebraic Bethe ansatz for the XXX chain with triangular boundaries and Gaudin model

Abstract

We implement fully the algebraic Bethe ansatz for the XXX Heisenberg spin chain in the case when both boundary matrices can be brought to the upper-triangular form. We define the Bethe vectors which yield the strikingly simple expression for the off shell action of the transfer matrix, deriving the spectrum and the corresponding Bethe equations. We explore further these results by obtaining the off shell action of the generating function of the Gaudin Hamiltonians on the Bethe vectors through the so-called quasi-classical limit.

arXiv comment31 pages; typos corrected

References in corpus (25)

• How Algebraic Bethe Ansatz works for integrable model
• Bethe Ansatz solution of the open XXZ chain with nondiagonal boundary terms
• Boundary K-matrices for the XYZ, XXZ AND XXX spin chains
• Off-diagonal Bethe ansatz solution of the XXX spin-chain with arbitrary boundary conditions
• Heisenberg XXX Model with General Boundaries: Eigenvectors from Algebraic Bethe Ansatz
• Bethe ansatz for the XXX-S chain with non-diagonal open boundaries
• Algebraic Bethe Ansatz for XYZ Gaudin model
• General boundary conditions for the sl(N) and sl(M|N) open spin chains
• Algebraic Bethe ansatz for open XXX model with triangular boundary matrices
• Solution of the SU(N) Vertex Model with Non-Diagonal Open Boundaries
• Exact solutions and elementary excitations in the XXZ spin chain with unparallel boundary fields
• $A_{n-1}$ Gaudin model with open boundaries
• On Integrable Models Related to the $osp(1,2)$ Gaudin Algebra
• Creation operators and Bethe vectors of the osp(1|2) Gaudin model
• Trigonometric osp(1|2) Gaudin model
• Quantum and Classical Integrable Systems
• $Z_n$ elliptic Gaudin model with open boundaries
• Algebraic Bethe ansatz for the six vertex model with upper triangular $K$-matrices
• Off-Shell Bethe Ansatz Equation for $osp(2|1)$ Gaudin Magnets
• Algebraic Bethe ansatz for the sl(2) Gaudin model with boundary
• Trigonometric sl(2) Gaudin model with boundary terms
• Determinant representations for scalar products of the XXZ Gaudin model with general boundary terms
• $sl(2|1{)}^{(2)}$ Gaudin Magnet and its associated Knizhnik-Zamolodchikov equation
• Jordanian deformation of the open XXX-spin chain
• Coordinate Bethe Ansätze for non-diagonal boundaries

Cited by in corpus (8)

• Modified algebraic Bethe ansatz for XXZ chain on the segment - I - triangular cases
• An integrable case of the p+ip pairing Hamiltonian interacting with its environment
• Non-compact quantum spin chains as integrable stochastic particle processes
• Algebraic Bethe ansatz for the sl(2) Gaudin model with boundary
• Eigenstates of triangularisable open XXX spin chains and closed-form solutions for the steady state of the open SSEP
• Algebraic Bethe ansatz for the XXZ Heisenberg spin chain with triangular boundaries and the corresponding Gaudin model
• Slavnov and Gaudin-Korepin formulas for models without $U(1)$ symmetry: the XXX chain on the segment
• Scalar product for the XXZ spin chain with general integrable boundaries