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Finite size properties of staggered $U_q[sl(2|1)]$ superspin chains

Based on the exact solution of the eigenvalue problem for the $U_q[sl(2|1)]$ vertex model built from alternating 3-dimensional fundamental and dual representations by means of the algebraic Bethe ansatz we investigate the ground state and low energy excitations of the corresponding mixed superspin chain for deformation parameter $q=\exp(-iγ/2)$. The model has a line of critical points with central charge $c=0$ and continua of conformal dimensions grouped into sectors with $γ$-dependent lower edges for $0\leγ<π/2$. The finite size scaling behaviour is consistent with a low energy effective theory consisting of one compact and one non-compact bosonic degree of freedom. In the 'ferromagnetic' regime $π<γ\le2π$ the critical theory has $c=-1$ with exponents varying continuously with the deformation parameter. Spin and charge degrees of freedom are separated in the finite size spectrum which coincides with that of the $U_q[osp(2|2)]$ spin chain. In the intermediate regime $π/2<γ<π$ the finite size scaling of the ground state energy depends on the deformation parameter.