Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:solv-int/9910008 · Journal of Mathematical Physics

Exact solution of the quantum Calogero–Gaudin system and of its q deformation

Fabio Musso, O. Ragnisco

Published Nov 1, 2000• 15 citations
arXivHTMLPDF

Abstract

A complete set of commuting observables for the Calogero–Gaudin system is diagonalized, and the explicit form of the corresponding eigenvalues and eigenfunctions is derived. We use a purely algebraic procedure exploiting the coalgebra invariance of the model; with the proper technical modifications this procedure can be applied to the q-deformed version of the model, which is then also exactly solved.

DOI
10.1063/1.1308508

Related papers

The spin-½ Calogero-Gaudin system and itsq-deformation

Fabio Musso, O. Ragnisco

The spin-½ Calogero-Gaudin system and its q -deformation are exactly solved: a complete set of commuting observables is diagonalized, and the corresponding eigenvectors and eigenvalues are explicitly calculated. The method of solution is purely algebraic and relies on the co-algebra symmetry of the model.

arXiv:nlin/0009001•Journal of Physics A Mathematical and General•Mar 19, 2001•12 citations

Exact solution of a supersymmetric Gaudin model

Julia Breiderhoff, Musso, Fabio, O. Ragnisco

A special case of the Gaudin model related to the superalgebra $osp(1,2)$ is investigated. An exact solution for the model in the spin-1/2 representation is presented. A complete set of commuting observables is diagonalized and the corresponding eigenvectors and eigenvalues are explicitly calculated. The approach used in this paper is based on the co-algebra symmetry of the model, already known from the spin-1/2 Calogero-Gaudin system.

arXiv:math-ph/0310003•Oct 3, 2003•1 citation

Exact solution to a supersymmetric Gaudin model

Julia Breiderhoff, Fabio Musso, O. Ragnisco

We investigate a special case of the Gaudin model related to the superalgebra osp(1,2). We present an exact solution to that system diagonalizing a complete set of commuting observables, and providing the corresponding eigenvectors and eigenvalues. The approach used in this paper is based on the co-algebra symmetry of the model, already known from the Calogero–Gaudin system.

Journal of Mathematical Physics•Feb 15, 2005•4 citations

Lie algebra deformations and the exact solutions of integrable quantum many-body systems

Yuan-Harng Lee

In this body of work, we will examine two classes of Lie algebra deformations and their appli- cation to the exact solutions of various quantum integrable systems. The first class of Lie algebra deformations are polynomial deformations of the A1 Lie algebra. We construct unitary representations of these algebras in terms of bosonic and spin operators as well as obtain their single-variable differential operator realizations. Using these results, we obtain the exact Bethe ansatz solutions of a variety of quantum integrable systems such as the Bose-Hubbard and Tavis-Cummings model. The second class of Lie algebra deformations are the so-called quasi-Gaudin algebra. This algebra was introduced to construct integrable systems which are only quasi-exactly solvable. Using a suitable representation this algebra, we obtain partial solutions for a class of bosonic models which do not preserve U(1) symmetry

•Jan 1, 2012•0 citations

EXACTLY SOLVABLE PAIRING MODEL USING AN EXTENSION OF THE RICHARDSON–GAUDIN APPROACH

A. B. Balantekin, T. DERELI, Y. PEHLIVAN

We introduce a new class of exactly solvable boson pairing models using the technique of Richardson and Gaudin. Analytical expressions for all energy eigenvalues and the first few energy eigenstates are given. In addition, another solution to Gaudin's equation is also mentioned. A relation with the Calogero–Sutherland model is suggested.

arXiv:nucl-th/0505023•International Journal of Modern Physics E•Feb 1, 2005•4 citations

Pairing interaction and its q-deformed versions

Sidney S. Avancini, Débora Peres Menezes

We investigate the behaviour of the pairing model within the context of quantum algebras. The pairing Hamiltonian is diagonalized exactly for different values of the deformation parameter q in systems with 8 and 50 particles. The same Hamiltonian is solved with the help of the coherent state variational method. We find that the variational method gives reliable results when compared with the exact ones. We also discuss the differences between the two deformation procedures.

Journal of Physics A Mathematical and General•Nov 21, 1993•7 citations
A complete set of commuting observables for the Calogero–Gaudin system is diagonalized, and the explicit form of the corresponding eigenvalues and eigenfunctions is derived. We use a purely algebraic procedure exploiting the coalgebra invariance of the model; with the proper technical modifications this procedure can be applied to the q-deformed version of the model, which is then also exactly solved.
A special case of the Gaudin model related to the superalgebra osp(1,2)osp(1,2)osp(1,2) is investigated. An exact solution for the model in the spin-1/2 representation is presented. A complete set of commuting observables is diagonalized and the corresponding eigenvectors and eigenvalues are explicitly calculated. The approach used in this paper is based on the co-algebra symmetry of the model, already known from the spin-1/2 Calogero-Gaudin system.
In this body of work, we will examine two classes of Lie algebra deformations and their appli- cation to the exact solutions of various quantum integrable systems. The first class of Lie algebra deformations are polynomial deformations of the A1 Lie algebra. We construct unitary representations of these algebras in terms of bosonic and spin operators as well as obtain their single-variable differential operator realizations. Using these results, we obtain the exact Bethe ansatz solutions of a variety of quantum integrable systems such as the Bose-Hubbard and Tavis-Cummings model. The second class of Lie algebra deformations are the so-called quasi-Gaudin algebra. This algebra was introduced to construct integrable systems which are only quasi-exactly solvable. Using a suitable representation this algebra, we obtain partial solutions for a class of bosonic models which do not preserve U(1) symmetry