Integrable open-boundary conditions for the supersymmetric t-J model. The quantum group invariant case

Abstract

We consider integrable open--boundary conditions for the supersymmetric t--J model commuting with the number operator $n$ and $S^z$. Four families, each one depending on two arbitrary parameters, are found. We find the relation between Sklyanin's method of constructing open boundary conditions and the one for the quantum group invariant case based on Markov traces. The eigenvalue problem is solved for the new cases by generalizing the Nested Algebraic Bethe ansatz of the quantum group invariant case (which is obtained as a special limit). For the quantum group invariant case the Bethe ansatz states are shown to be highest weights of $sp{l}_q(2,1)$.

Latex, 24 pages. Some new comments and references. Final version to appear in Nucl. Phys. B

References in corpus (7)

• Reaction-Diffusion Processes, Critical Dynamics and Quantum Chains
• Boundary K-Matrices for the Six Vertex and the n(2n-1) A_{n-1} Vertex Models
• Addendum to ``Integrability of Open Spin Chains with Quantum Algebra Symmetry''
• Exact solution of the $S{U}_q(n)$ invariant quantum spin chains
• Bethe Ansatz and Quantum Groups: The Light--Cone Approach. II. From RSOS($p+1$) models to $p-$restricted Sine--Gordon Field Theories
• Free Fermionic Elliptic Reflection Matrices and Quantum Group Invariance
• On Integrable Quantum Group Invariant Antiferromagnets

Cited by in corpus (56)

• Interaction-Round-a-Face Models with Fixed Boundary Conditions: The ABF Fusion Hierarchy
• Baxter's Q-operators for supersymmetric spin chains
• Row Transfer Matrix Functional Relations for Baxter's Eight-Vertex and Six-Vertex Models with Open Boundaries Via More General Reflection Matrices
• The Supersymmetric t-J Model with a Boundary
• Exact Bethe Ansatz solution for $A_{n-1}$ chains with non-$S{U}_q(n)$ invariant open boundary conditions
• Integrable open-boundary conditions for the $q$-deformed supersymmetric $U$ model of strongly correlated electrons
• Solution of the SU(N) Vertex Model with Non-Diagonal Open Boundaries
• Exact Boundary Critical Exponents and Tunneling Effect in Integrable Models for Quantum Wires
• Open t-J chain with boundary impurities
• Direct Calculation of the Boundary $S$ Matrix for the Open Heisenberg Chain
• New solutions to the Reflection Equation and the projecting method
• Analytical Bethe Ansatz for closed and open gl(M|N) super-spin chains in arbitrary representations and for any Dynkin diagram
• Bethe Ansatz equations and exact S matrices for the osp(M|2n) open super spin chain
• Graded reflection equation algebras and integrable Kondo impurities in the one-dimensional t-J model
• Exact diagonalization of the quantum supersymmetric $S{U}_q(n|m)$ model
• The Highest Weight Property for the $S{U}_q(n)$ Invariant Spin Chains
• Integrability of the $D_n^2$ vertex models with open boundary
• The Bethe Ansatz Equations for Reflecting Magnons
• Classical and Quantum sl(1|2) Superalgebras, Casimir Operators and Quantum Chain Hamiltonians
• Hidden Kondo Effect in a Correlated Electron Chain
• Exact solution of the one-dimensional super-symmetric t-J model with unparallel boundary fields
• Quantum Group Invariant Supersymmetric t-J Model with periodic boundary conditions
• Algebraic Bethe ansatz for integrable Kondo impurities in the one-dimensional supersymmetric t-J model
• Spectrum of the supersymmetric t-J model with non-diagonal open boundaries
• Exact diagonalization of the generalized supersymmetric t-J model with boundaries
• Staggered Anisotropy Parameter Modification of the Anisotropic $t-J$ Model
• Surveying the quantum group symmetries of integrable open spin chains
• Exact solution for the Bariev model with boundary fields
• Spin excitations in the integrable open quantum group invariant supersymmetric t-J model
• Non-diagonal boundary conditions for gl(1|1) super spin chains
• A Bethe ansatz solution for the closed $U_q[sl(2)]$ Temperley-Lieb quantum spin chains
• Bethe ansatz solution of a closed spin 1 XXZ Heisenberg chain with quantum algebra symmetry
• An open-boundary integrable model of three coupled XY spin chains
• Reflection matrices for the $U_q[sl(m|n{)}^{(1)}]$ vertex model
• Exact Solution of a Electron System Combining Two Different t-J Models
• Boundary Kondo impurities in the generalized supersymmetric t-J model
• Quantum integrability and exact solution of the supersymmetric U model with boundary terms
• Bethe Ansatz solution of the small polaron with nondiagonal boundary terms
• Truncation identities for the small polaron fusion hierarchy
• Two Magnetic Impurities with Arbitrary Spins in Open Boundary t-J Model
• Integrable open-boundary conditions for the q-deformed extended Hubbard model
• Quantum group symmetries and completeness for A_{2n}^(2) open spin chains
• Integrable Kondo impurities in one-dimensional extended Hubbard models
• Boundary K-matrices and the Lax pair for 1D open XYZ spin-chain
• Algebraic Bethe ansatz for the supersymmetric $t-J$ model with reflecting boundary conditions
• Quantum-classical correspondence for gl(1|1) supersymmetric Gaudin magnet with boundary
• Lax Operator for the Quantised Orthosymplectic Superalgebra U_q[osp(2|n)]
• Integrable eight-state supersymmetric $U$ model with boundary terms and its Bethe ansatz solution
• Bethe Ansatz solutions for Temperley-Lieb Quantum Spin Chains
• A note on open-chain transfer matrices from q-deformed su(2|2) S-matrices
• Solutions to the Yang-Baxter Equation and Casimir Invariants for the Quantised Orthosymplectic Superalgebra
• Eigenvalues of Casimir invariants for Uq[osp(m|n)]
• Surface energy of the one-dimensional supersymmetric $t-J$ model with general integrable boundary terms in the antiferromagnetic sector
• On the Bethe states of the one-dimensional supersymmetric t-J model with generic open boundaries
• Interplay between a quantum impurity and a boundary field in the SUSY t-J model
• On the ${\mathcal{U}}_q[osp(1|2)]$ Temperley-Lieb model