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

Journal of Physics A Mathematical and General

Connection between Yangian symmetry and the quantum inverse scattering method

Shuichi Murakami, Miki Wadati

Published Dec 21, 1996• 31 citations
Publisher

Abstract

The quantum nonlinear Schrödinger model with two-component fermions exhibits a Yangian symmetry when considered on an infinite interval. We construct the generators of the Yangian using Dunkl operators. We show an equivalence between the monodromy matrix constructed from the Dunkl operators and that of the quantum inverse scattering method. Under the Yangian algebra the space of states with a fixed particle number forms a tensor product representation of fundamental representations.

DOI
10.1088/0305-4470/29/24/015

Related papers

YANGIAN SYMMETRY OF THE TWO-COMPONENT FERMIONIC NONLINEAR SCHRÖDINGER MODEL

Shuichi Murakami, Miki Wadati

The quantum nonlinear Schrödinger model with two-component fermions exhibits a Yangian symmetry when considered on an infinite interval. We construct the generators of the Yangian using one representation of the degenerate affine Hecke algebra. We discuss the connection between the Yangian symmetry and the quantum inverse scattering method. Under the Yangian algebra the space of states with a fixed particle number forms a tensor product representation of fundamental representations.

International Journal of Modern Physics B•Jun 30, 1996•0 citations

Yangian Symmetry of theδ-Function Fermi Gas

Shuichi Murakami, Miki Wadati

The quantum nonlinear Schrödinger model with two-component fermions exhibits a Yangian symmetry when considered on an infinite interval. We construct the generators of the Yangian using one representation of the degenerate affine Hecke algebra. We discuss the connection between the Yangian symmetry and the quantum inverse scattering method. Under the Yangian algebra the space of states with a fixed particle number forms a tensor product representation of fundamental representations.

Journal of the Physical Society of Japan•May 15, 1996•14 citations

Yangian Symmetry and Quantum Inverse Scattering Method for the One-Dimensional Hubbard Model

Murakami, S, Gohmann, F, 村上修一 +1 more

We develop the quantum inverse scattering method for the one-dimensional Hubbard model on the infinite interval at zero density. R-matrix and monodromy matrix are obtained as limits from their known counterparts on the finite interval. The R-matrix greatly simplifies in the considered limit. The new R-matrix contains a submatrix which turns into the rational R-matrix of the XXX-chain by an appropriate reparametrization. The corresponding submatrix of the monodromy matrix thus provides a representation of the Y(su(2)) Yangian. From its quantum determinant we obtain an infinite series of mutually commuting Yangian invariant operators which includes the Hamiltonian. Keywords Hubbard model, quantum inverse scattering, Yangian z E-mail:murakami@appi.t.u-tokyo.ac.jp x E-mail:frank@monet.phys.s.u-tokyo.ac.jp -- Address from Oct. 1996: Physikalisches Institut der Universitat Bayreuth, TP1, 95440 Bayreuth, Germany. 1 Introduction Among the exactly solvable 1d quantum systems the Hubbard...

•Jan 1, 1996•20 citations

Y(so(5)) symmetry of the nonlinear Schrödinger model with four-components

Hong-Biao Zhang, Mo-Lin Ge, Kang Xue

The quantum nonlinear Schrödinger model with four-component fermions exhibits a Y ( so (5)) symmetry when considered on an infinite interval. The constructed generators of the Yangian are proved to satisfy the Drinfel'd formula and, furthermore, the RTT relation with the general form of a rational R -matrix given by Yang-Baxterization associated with so (5) algebraic structure.

arXiv:math-ph/0111030•Journal of Physics A Mathematical and General•Jan 18, 2001•1 citation

IntegrableN-particle Hamiltonians with Yangian or reflection algebra symmetry

Vincent Caudrelier, Nicolas Crampé

We use the Dunkl operator approach to construct one-dimensional integrable models describing N particles with internal degrees of freedom. These models are described by a general Hamiltonian belonging to the centre of the Yangian or the reflection algebra, which ensures that they admit the corresponding symmetry. In particular, the open problem of the symmetry is answered for the B N -type Sutherland model with spin and for a generalized B N -type nonlinear Schrödinger Hamiltonian.

arXiv:math-ph/0310028•Journal of Physics A Mathematical and General•Jun 3, 2004•16 citations

Quantum inverse scattering method for the nonlinear Schrodinger model of fermions with attractive interaction

Haitao Fan, Fu‐Cho Pu, Bao‐Heng Zhao

The quantum inverse scattering method is applied to the nonlinear Schrodinger model of fermions with attractive interactions. Both scattering and bound-state operators are constructed. Among state operators, there are generators of infinitely many conserved quantities and the creators of the eigenstates of these quantities. The commutation relations and the eigenvalues of physical interest are calculated. The quantum Gelfand-Levitan equations are established. The Fourier transform of the connected part of the 4-point Green function and the two body S matrix are calculated explicitly.

Journal of Physics A Mathematical and General•Nov 21, 1989•3 citations
The quantum nonlinear Schrödinger model with two-component fermions exhibits a Yangian symmetry when considered on an infinite interval. We construct the generators of the Yangian using Dunkl operators. We show an equivalence between the monodromy matrix constructed from the Dunkl operators and that of the quantum inverse scattering method. Under the Yangian algebra the space of states with a fixed particle number forms a tensor product representation of fundamental representations.
We develop the quantum inverse scattering method for the one-dimensional Hubbard model on the infinite interval at zero density. R-matrix and monodromy matrix are obtained as limits from their known counterparts on the finite interval. The R-matrix greatly simplifies in the considered limit. The new R-matrix contains a submatrix which turns into the rational R-matrix of the XXX-chain by an appropriate reparametrization. The corresponding submatrix of the monodromy matrix thus provides a representation of the Y(su(2)) Yangian. From its quantum determinant we obtain an infinite series of mutually commuting Yangian invariant operators which includes the Hamiltonian. Keywords Hubbard model, quantum inverse scattering, Yangian z E-mail:murakami@appi.t.u-tokyo.ac.jp x E-mail:frank@monet.phys.s.u-tokyo.ac.jp -- Address from Oct. 1996: Physikalisches Institut der Universitat Bayreuth, TP1, 95440 Bayreuth, Germany. 1 Introduction Among the exactly solvable 1d quantum systems the Hubbard...
The quantum inverse scattering method is applied to the nonlinear Schrodinger model of fermions with attractive interactions. Both scattering and bound-state operators are constructed. Among state operators, there are generators of infinitely many conserved quantities and the creators of the eigenstates of these quantities. The commutation relations and the eigenvalues of physical interest are calculated. The quantum Gelfand-Levitan equations are established. The Fourier transform of the connected part of the 4-point Green function and the two body S matrix are calculated explicitly.