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[en] The low energy spectrum of a spin chain with supergroup symmetry is studied based on the Bethe ansatz solution of the related vertex model. This model is a lattice realization of intersecting loops in two dimensions with loop fugacity which provides a framework to study the critical properties of the unusual low temperature Goldstone phase of the sigma model for in the context of an integrable model. Our finite-size analysis provides strong evidence for the existence of continua of scaling dimensions, the lowest of them starting at the ground state. Based on our data we conjecture that the so-called watermelon correlation functions decay logarithmically with exponents related to the quadratic Casimir operator of . The presence of a continuous spectrum is not affected by a change to the boundary conditions although the density of states in the continua appears to be modified.
[en] We construct a family of integrable vertex model based on the typical four-dimensional representations of the quantum group deformation of the Lie superalgebra sl(2|1). Upon alternation of such a representation with its dual this model gives rise to a mixed superspin Hamiltonian with local interactions depending on the representation parameter ±b and the deformation parameter γ. As a subsector this model contains integrable vertex models with ordinary symmetries for twisted boundary conditions. The thermodynamic limit and low energy properties of the mixed superspin chain are studied using a combination of analytical and numerical methods. Based on these results we identify the phases realized in this system as a function of the parameters b and γ. The different phases are characterized by the operator content of the corresponding critical theory. Only part of the spectrum of this effective theory can be understood in terms of the U(1) symmetries related to the physical degrees of freedom corresponding to spin and charge. The other modes lead to logarithmic finite-size corrections in the spectrum of the theory.
[en] This paper is concerned with the investigation of the massless regime of an integrable spin chain based on the quantum group deformation of the superalgebra. The finite-size properties of the eigenspectra are computed by solving the respective Bethe ansatz equations for large system sizes allowing us to uncover the low-lying critical exponents. We present evidences that critical exponents appear to be built in terms of composites of anomalous dimensions of two Coulomb gases with distinct radii and the exponents associated to degrees of freedom. This view is supported by the fact that the XXZ integrable chain spectrum is present in some of the sectors of our superspin chain at a particular value of the deformation parameter. We find that the fine structure of finite-size effects is very rich for a typical anisotropic spin chain. In fact, we argue on the existence of a family of states with the same conformal dimension whose lattice degeneracies are apparently lifted by logarithmic corrections. On the other hand we also report on states of the spectrum whose finite-size corrections seem to be governed by a power law behaviour. We finally observe that under toroidal boundary conditions the ground state dependence on the twist angle has two distinct analytical structures.
[en] Based on the exact solution of the eigenvalue problem for the Uq[sl(2|1)] vertex model built from alternating three-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≤γ<π/2. The finite size scaling behavior 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≤2π 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 Uq[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.