Algebraic Bethe ansatz for the sl(2) Gaudin model with boundary

Abstract

Following Sklyanin's proposal in the periodic case, we derive the generating function of the Gaudin Hamiltonians with boundary terms. Our derivation is based on the quasi-classical expansion of the linear combination of the transfer matrix of the XXX Heisenberg spin chain and the central element, the so-called Sklyanin determinant. The corresponding Gaudin Hamiltonians with boundary terms are obtained as the residues of the generating function. By defining the appropriate Bethe vectors which yield strikingly simple off shell action of the generating function, we fully implement the algebraic Bethe ansatz, obtaining the spectrum of the generating function and the corresponding Bethe equations.

arXiv comment31 pages; presentation improved. arXiv admin note: substantial text overlap with arXiv:1405.7398

References in corpus (27)

• How Algebraic Bethe Ansatz works for integrable model
• Gaudin Model, Bethe Ansatz and Critical Level
• Bethe Ansatz solution of the open XXZ chain with nondiagonal boundary terms
• Boundary K-matrices for the XYZ, XXZ AND XXX spin chains
• Quasiclassical asymptotics of solutions to the KZ equations
• 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
• Heisenberg XXX Model with General Boundaries: Eigenvectors from Algebraic Bethe Ansatz
• Off-Shell Bethe Ansatz Equation for Gaudin Magnets and Solutions of Knizhnik-Zamolodchikov Equations
• Bethe ansatz for the XXX-S chain with non-diagonal open boundaries
• Algebraic Bethe Ansatz for XYZ Gaudin model
• Algebraic Bethe ansatz for open XXX model with triangular boundary matrices
• 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
• Quantum and Classical Integrable Systems
• Trigonometric osp(1|2) Gaudin model
• $Z_n$ elliptic Gaudin model with open boundaries
• Algebraic Bethe ansatz for the XXX chain with triangular boundaries and Gaudin model
• Algebraic Bethe ansatz for the six vertex model with upper triangular $K$-matrices
• Off-Shell Bethe Ansatz Equation for $osp(2|1)$ Gaudin Magnets
• Determinant representations for scalar products of the XXZ Gaudin model with general boundary terms
• Trigonometric sl(2) Gaudin model with boundary terms
• $sl(2|1{)}^{(2)}$ Gaudin Magnet and its associated Knizhnik-Zamolodchikov equation
• Coordinate Bethe Ansätze for non-diagonal boundaries
• Analytical Bethe ansatz in gl(N) spin chains

Cited by in corpus (3)

• An integrable case of the p+ip pairing Hamiltonian interacting with its environment
• Algebraic Bethe ansatz for the XXX chain with triangular boundaries and Gaudin model
• Algebraic Bethe ansatz for the XXZ Heisenberg spin chain with triangular boundaries and the corresponding Gaudin model