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

Chinese Physics Letters

Rational SU(N) Gaudin Model

Junpeng Cao, Bo-Yu Hou, Rui‐Hong Yue

Published May 3, 2001• 0 citations
Publisher

Abstract

We propose the eigenstates and eigenvalues of Hamiltonians of the rational SU ( N ) Gaudin model based on the quasi-classical limit of the SU ( N ) chain under the periodic boundary condition. Using the quantum inverse scattering method, we also obtain the eigenvalues of the generation function of the rational SU ( N ) Gaudin model.
DOI
10.1088/0256-307x/18/6/301

Related papers

Trigonometric SU(N) Gaudin model

Junpeng Cao, Bo-Yu Hou, Yue Rui-Hong

In this paper, we obtain the eigenstates and the eigenvalues of the Hamiltonians of the trigonometric SU(N) Gaudin model based on the quasi-classical limit of the trigonometric SU(N) chain with the periodic boundary condition. By using the quantum inverse scattering method, we also obtain the eigenvalues of the generating function of the trigonometric SU(N) Gaudin model.

Chinese Physics•Sep 25, 2001•1 citation

Rational SU(3) Gaudin Model

Junpeng Cao, Bo-Yu Hou, Rui‐Hong Yue

The Hamiltonians of the SU(3) Gaudin model are constructed based on the nonrelativistic limit of the SU(3) chain. After the quantum determinant being well defined, the eigenvectors and eigenvalues of the Hamiltonians of the SU(3) Gaudin model are given. These results can be generalized to any number of constituting spins (SU(N)).

Communications in Theoretical Physics•Aug 15, 2001•0 citations

GeneralizedSUq(1|2) Gaudin model

Jun-peng Cao, Bo-Yu Hou, Rui‐Hong Yue

In this paper we propose the Hamiltonians of the generalized SU q (1|2) Gaudin model corresponding to the periodic generalized t - J model. With the help of the well defined graded quantum determinant, we obtain the eigenstate and eigenvalues of the generating function and the Hamiltonians of the Gaudin model in the fermionic background in the framework of the graded quantum inverse scattering method. The Bethe ansatz equations are also obtained.

Journal of Physics A Mathematical and General•Apr 27, 2001•1 citation

Richardson-Gaudin models from the Boundary Quantum Inverse Scattering Method

Inna Lukyanenko

Richardson–Gaudin models are a class of quantum integrable models connected to many physical systems, including pairing Hamiltonians from the theory of superconductivity. They can be obtained in the quasi-classical limit of the Quantum Inverse Scattering Method, which is based on an R-matrix and a Lax operator satisfying the Yang-Baxter equation. They can also be obtained from the Boundary Quantum Inverse Scattering Method, which relies on solutions of the reflection equations known as K-matrices. In this thesis we study these latter models systematically, explore the connections betweenthem and investigate the interpretation of the “boundary”.First of all, we consider Richardson–Gaudin models obtained from the spin-1/2 su(2) Boundary Quantum Inverse Scattering Method with diagonal K-matrices. We prove that the trigonometric boundary construction is equivalent to its rational limit, through a change of variables, rescaling, and a basis transformation. Moreover, we prove that the twisted-periodic and boundary constructions are equivalent in the trigonometric case, but not in the rational limit. Thus, including the “boundary” does not lead to a new model in this case.Next, we investigate Richardson–Gaudin models obtained from the spin-1/2 su(2) Boundary Quantum Inverse Scattering Method with non-diagonal K-matrices. Here the situation is different. The conserved operators in the boundary construction are no longer equivalent to the ones in the twisted-periodic construction. Also, the rational and the trigonometric boundary constructions are not equivalent. In the rational case this allows us to construct a generalisation of the p+ip pairing Hamiltonian with external interaction terms. In the trigonometric case the expressions for the conserved operators involve several free parameters, which can be adjusted to construct a variety of Hamiltonians. This result offers opportunities for future investigations.Finally, we study the case of the q-deformed bosonic Lax operator. This case is much more challenging than the case of the spin Lax operator. It is not straightforward to define the rational and quasi-classical limits of the bosonic Lax operator. Even after making modifications to the Lax operator for these limits to be well defined, it turns out that the limits do not commute. We state some open questions for future work.

•Aug 29, 2016•0 citations

Supersymmetric SU (1|2) Gaudin model

Junpeng Cao, Bo-Yu Hou, Rui‐Hong Yue

In this paper, we propose a supersymmetric SU (1|2) Gaudin model and have derived its eigenvalues. We also present the well-defined eigenstates through the quasi-classical limit of the eigenstates in the supersymmetric t-J model.

Chinese Physics•Jan 22, 2001•0 citations

Thesl(2|1)(2)Gaudin magnet with diagonal boundary terms

A. Lima-Santos

This work is concerned with the quasi-classical limit of the boundary quantum inverse scattering method for the twisted sl (2|1) (2) vertex model with diagonal K -matrices. In this limit Gaudin’s Hamiltonians with diagonal boundary terms are presented and diagonalized.

Journal of Statistical Mechanics Theory and Experiment•Jul 16, 2009•7 citations
Richardson–Gaudin models are a class of quantum integrable models connected to many physical systems, including pairing Hamiltonians from the theory of superconductivity. They can be obtained in the quasi-classical limit of the Quantum Inverse Scattering Method, which is based on an R-matrix and a Lax operator satisfying the Yang-Baxter equation. They can also be obtained from the Boundary Quantum Inverse Scattering Method, which relies on solutions of the reflection equations known as K-matrices. In this thesis we study these latter models systematically, explore the connections betweenthem and investigate the interpretation of the “boundary”.First of all, we consider Richardson–Gaudin models obtained from the spin-1/2 su(2) Boundary Quantum Inverse Scattering Method with diagonal K-matrices. We prove that the trigonometric boundary construction is equivalent to its rational limit, through a change of variables, rescaling, and a basis transformation. Moreover, we prove that the twisted-periodic and boundary constructions are equivalent in the trigonometric case, but not in the rational limit. Thus, including the “boundary” does not lead to a new model in this case.Next, we investigate Richardson–Gaudin models obtained from the spin-1/2 su(2) Boundary Quantum Inverse Scattering Method with non-diagonal K-matrices. Here the situation is different. The conserved operators in the boundary construction are no longer equivalent to the ones in the twisted-periodic construction. Also, the rational and the trigonometric boundary constructions are not equivalent. In the rational case this allows us to construct a generalisation of the p+ip pairing Hamiltonian with external interaction terms. In the trigonometric case the expressions for the conserved operators involve several free parameters, which can be adjusted to construct a variety of Hamiltonians. This result offers opportunities for future investigations.Finally, we study the case of the q-deformed bosonic Lax operator. This case is much more challenging than the case of the spin Lax operator. It is not straightforward to define the rational and quasi-classical limits of the bosonic Lax operator. Even after making modifications to the Lax operator for these limits to be well defined, it turns out that the limits do not commute. We state some open questions for future work.