arXiv subjects

N. Cirilo António

Publications and source records attributed to N. Cirilo António.

4 recordsLinked to original sources

arXiv2015

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

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.

nlin.SI↗

arXiv2014

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

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.

math-ph↗

arXiv2013

Trigonometric sl(2) Gaudin model with boundary terms

We review the derivation of the Gaudin model with integrable boundaries. Starting from the non-symmetric R-matrix of the inhomogeneous spin-1/2 XXZ chain and generic solutions of the reflection equation and the dual reflection equation, the corresponding Gaudin Hamiltonians with boundary terms are calculated. An alternative derivation based on the so-called classical reflection equation is discussed.

nlin.SI↗

arXiv2013

Jordanian deformation of the open sl(2) Gaudin model

We derive the deformed sl(2) Gaudin model with integrable boundaries. Starting from the Jordanian deformation of the SL(2)-invariant Yang R-matrix and generic solutions of the associated reflection equation and the dual reflection equation, the corresponding inhomogeneous spin-1/2 XXX chain is obtained. The quasi-classical expansion of the transfer matrix yields the deformed sl(2) Gaudin Hamiltonians with boundary terms.

nlin.SI↗