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理论物理通讯：英文版

The Boundary States of the q-Deformed Supersymmetric t-J Model with a Boundary

Yang, Wenli, Zhen, Yi Yi

Published Jan 1, 2001• 0 citations
OpenAlex

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 Uq[sl(2|1)]. We give the bosonization of the boundary states.``

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Boundary state of Uq(gl^(N∣N))U_q(\hat{gl}(N|N))Uq​(gl^​(N∣N)) analog of half-infinite t−Jt-Jt−J model
The Uq(gl^(N∣N))U_q(\hat{gl}(N|N))Uq​(gl^​(N∣N))-analog of the half-infinite t−Jt-Jt−J model with a boundary is considered by using the vertex operator approach. We find explicit bosonic formula of the boundary state in the integrable highest-weight module over the quantum superalgebra Uq(gl^(N∣N))U_q(\hat{gl}(N|N))Uq​(gl^​(N∣N)).
Upon introducing a one-parameter quadratic deformation of the q-boson algebra and a diagonal perturbation at the end point, we arrive at a semi-infinite q-boson system with a two-parameter boundary interaction. The eigenfunctions are shown to be given by Macdonald’s hyperoctahedral Hall–Littlewood functions of type BC. It follows that the n-particle spectrum is bounded and absolutely continuous and that the corresponding scattering matrix factorizes as a product of two-particle bulk and one-particle boundary scattering matrices.