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Integrable open-boundary conditions for the supersymmetric t-J model. The quantum group invariant case  [PDF]
A. González-Ruiz
Physics , 1994, DOI: 10.1016/0550-3213(94)90403-0
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 $spl_{q}(2,1)$.
Anti-Periodic Boundary Conditions in Supersymmetric DLCQ  [PDF]
S. Pinsky,U. Trittmann
Physics , 2000, DOI: 10.1103/PhysRevD.62.087701
Abstract: It is of considerable importance to have a numerical method for solving supersymmetric theories that can support a non-zero central charge. The central charge in supersymmetric theories is in general a boundary integral and therefore vanishes when one uses periodic boundary conditions. One is therefore prevented from studying BPS states in the standard supersymmetric formulation of DLCQ (SDLCQ). We present a novel formulation of SDLCQ where the fields satisfy anti-periodic boundary conditions. The Hamiltonian is written as the anti-commutator of two charges, as in SDLCQ. The anti-periodic SDLCQ we consider breaks supersymmetry at finite resolution, but requires no renormalization and becomes supersymmetric in the continuum limit. In principle, this method could be used to study BPS states. However, we find its convergence to be disappointingly slow.
The Supersymmetric t-J Model with a Boundary  [PDF]
Fabian H. L. Essler
Physics , 1996, DOI: 10.1088/0305-4470/29/19/006
Abstract: An open supersymmetric t-J chain with boundary fields is studied by means of the Bethe Ansatz. Ground state properties for the case of an almost half-filled band and a bulk magnetic field are determined. Boundary susceptibilities are calculated as functions of the boundary fields. The effects of the boundary on excitations are investigated by constructing the exact boundary S-matrix. From the analytic structure of the boundary S-matrices one deduces that holons can form boundary bound states for sufficiently strong boundary fields.
Boundary Kondo impurities in the generalized supersymmetric t-J model  [PDF]
Heng Fan,Miki Wadati,Rui-hong Yue
Physics , 1999, DOI: 10.1088/0305-4470/33/35/307
Abstract: We study the generalized supersymmetric t-J model with Kondo impurities in the boundaries. We first construct the higher spin operator K-matrix for the XXZ Heisenberg chain. Setting the boundary parameter to be a special value, we find a higher spin reflecting K-matrix for the supersymmetric t-J model. By using the Quantum Inverse Scattering Method, we obtain the eigenvalue and the corresponding Bethe ansatz equations.
Crystal potentials under invariant periodic boundary conditions at infinity  [PDF]
Eugene V. Kholopov
Physics , 2002,
Abstract: The definiteness of bulk electrostatic potentials in solids under periodic boundary conditions defined in an invariant manner has been proved in the general case of triclinic symmetry. Some principal consequences following from the universal potential correction arising are discussed briefly.
q-deformed Supersymmetric t-J Model with a Boundary  [PDF]
Bo-Yu Hou,Wen-Li Yang,Yao-Zhong Zhang,Yi Zhen
Physics , 2001, DOI: 10.1088/0305-4470/35/11/306
Abstract: The q-deformed supersymmetric t-J model on a semi-infinite lattice is diagonalized by using the level-one vertex operators of the quantum affine superalgebra $U_q[\hat{sl(2|1)}]$. We give the bosonization of the boundary states. We give an integral expression of the correlation functions of the boundary model, and derive the difference equations which they satisfy.
Supersymmetric t-J Gaudin Models and KZ Equations  [PDF]
Mark D. Gould,Yao-Zhong Zhang,Shao-You Zhao
Physics , 2002, DOI: 10.1088/0305-4470/35/44/308
Abstract: Supersymmetric t-J Gaudin models with both periodic and open boundary conditions are constructed and diagonalized by means of the algebraic Bethe ansatz method. Off-shell Bethe ansatz equations of the Gaudin systems are derived, and used to construct and solve the KZ equations associated with $sl(2|1)^{(1)}$ superalgebra.
Algebraic Bethe ansatz for the supersymmetric $t-J$ model with reflecting boundary conditions  [PDF]
Heng Fan,Bo-yu Hou,Kang-jie Shi
Physics , 1998, DOI: 10.1016/S0550-3213(98)00763-9
Abstract: In the framework of the graded quantum inverse scattering method (QISM), we obtain the eigenvalues and eigenvectors of the supersymmetric $t-J$ model with reflecting boundary conditions in FFB background. The corresponding Bethe ansatz equations are obtained.
Spin excitations in the integrable open quantum group invariant supersymmetric t-J model  [PDF]
Y. -K. Zhou,M. T. Batchelor
Physics , 1996, DOI: 10.1016/S0550-3213(97)00106-5
Abstract: The integrable quantum group $spl_q(2,1)$-invariant supersymmetric t-J model with open boundaries is studied via an analytic treatment of the Bethe equations. An $su(2)$ feature is seen to hold for states at or close to half-filling. For these states the eigenvalues of the transfer matrix of the t-J model satisfy a set of $su(2)$ functional relations. The finite-size corrections to the relevant eigenvalues, and thus the surface effect on the spin excitations, have been calculated analytically by solving the functional relations.
Integrabilities of the long range t-J model of twisted boundary condition  [PDF]
J. T. Liu,D. F. Wang
Physics , 1996, DOI: 10.1103/PhysRevB.55.R3344
Abstract: The integrability of the one-dimensional long range supersymmetric t-J model has previously been established for both open systems and those closed by periodic boundary conditions through explicit construction of its integrals of motion. Recently the system has been extended to include the effect of magnetic flux, which gives rise to a closed chain with twisted boundary conditions. While the t-J model with twisted boundary conditions has been solved for the ground state and full energy spectrum, proof of its integrability has so far been lacking. In this letter we extend the proof of integrability of the long range supersymmetric t-J model and its SU(m|n) generalization to include the case of twisted boundary conditions.
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