Twisted Quantum Affine Superalgebra Uq[sl(2|2)⁽²⁾], Uq[osp(2|2)] Invariant R-matrices and a New Integrable Electronic Model

Original · EN

We describe the twisted affine superalgebra sl(2|2)⁽²⁾ and its quantized version Uq[sl(2|2)⁽²⁾]. We investigate the tensor product representation of the 4-dimensional grade star representation for the fixed point subsuperalgebra Uq[osp(2|2)]. We work out the tensor product decomposition explicitly and find the decomposition is not completely reducible. Associated with this 4-dimensional grade star representation we derive two Uq[osp(2|2)] invariant R-matrices: one of them corresponds to Uq[sl(2|2)⁽²⁾] and the other to Uq[osp(2|2)⁽¹⁾]. Using the R-matrix for Uq[sl(2|2)⁽²⁾], we construct a new Uq[osp(2|2)] invariant strongly correlated electronic model, which is integrable in one dimension. Interestingly, this model reduces, in the q=1 limit, to the one proposed by Essler et al which has a larger, sl(2|2), symmetry.