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A. Lima-Santos

Publications and source records attributed to A. Lima-Santos.

46 records · Page 3Linked to original sources
arXiv1999

Osp(1|2) Off-shell Bethe Ansatz Equations

The semiclassical limit of the algebraic quantum inverse scattering method is used to solve the theory of the Gaudin model. Via Off-shell Bethe ansatz equations of an integrable representation of the graded osp(1|2) vertex model we find the spectrum of N-1 independent Hamiltonians of Gaudin. Integral representations of the N-point correlators are presented as solutions of the Knizhnik-Zamolodchikov equation. These results are extended for highest representations of the osp(1|2) Gaudin algebra.

solv-int↗
arXiv1999

Bethe Ansatze for 19-vertex Models

The nineteen-vertex models of Zamolodchikov-Fateev, Izergin-Korepin and the supersymmetric osp(1|2) with periodic boundary conditions are studied. We find the spectrum of these quantum spin chains using the Coordinate Bethe Ansatz. The approche is a suitable parametrization of their wavefunctions. We also applied the Algebraic Bethe Ansatz in order to obtain the eigenvalues and eigenvectors of the corresponding transfer matrices.

hep-th↗
arXiv1998

On fusion algebra of chiral $SU(N)_{k}$ models

We discuss some algebraic setting of chiral $SU(N)_{k}$ models in terms of the statistical dimensions of their fields. In particular, the conformal dimensions and the central charge of the chiral $SU(N)_{k}$ models are calculated from their braid matrices. Futhermore, at level K=2, we present the characteristic polynomials of their fusion matrices in a factored form.

solv-int↗
arXiv1998

Polynomial rings of the chiral $SU(N)_{2}$ models

Via explicit diagonalization of the chiral $SU(N)_{2}$ fusion matrices, we discuss the possibility of representing the fusion ring of the chiral SU(N) models, at level K=2, by a polynomial ring in a single variable when $N$ is odd and by a polynomial ring in two variables when $N$ is even.

solv-int↗
arXiv1998

Exact solutions of graded Temperley-Lieb Hamiltonians

Orthosympletic Hamiltonians derived from representations of the Temperley-Lieb algebra are presented and solved via the coordinate Bethe Ansatz. The spectra of these Hamiltonians are obtained using open and closed boundary conditions.

hep-th↗
arXiv1998

Knizhnik-Zamolodchikov-Bernard equations connected with the eight-vertex model

Using quasiclassical limit of Baxter's 8 - vertex R - matrix, an elliptic generalization of the Knizhnik-Zamolodchikov equation is constructed. Via Off-Shell Bethe ansatz an integrable representation for this equation is obtained. It is shown that there exists a gauge transformation connecting this equation with Knizhnik-Zamolodchikov-Bernard equation for SU(2)-WZNW model on torus.

solv-int↗
arXiv1995

Exact solution of A-D Temperley-Lieb Models

We solve for the spectrum of quantum spin chains based on representations of the Temperley-Lieb algebra associated with the quantum groups ${\cal U}_q(X_n } for $X_n = A_1,B_n,C_n$ and $D_n$. We employ a generalization of the coordinate Bethe-Ansatz developed previously for the deformed biquadratic spin one chain. As expected, all these models have equivalent spectra, i.e. they differ only in the degeneracy of their eigenvalues. This is true for finite length and open boundary conditions. For periodic boundary conditions the spectra of the lower dimensional representations are containded entirely in the higher dimensional ones. The Bethe states are highest weight states of the quantum group, except for some states with energy zero.

cond-mat↗