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

Abstract

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 $q=\exp(-i\gamma/2)$. The model has a line of critical points with central charge $c=0$ and continua of conformal dimensions grouped into sectors with $\gamma$-dependent lower edges for $0\le\gamma<\pi/2$. 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 $\pi<\gamma\le2\pi$ 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 $\pi/2<\gamma<\pi$ the finite size scaling of the ground state energy depends on the deformation parameter.