Abstract
This paper is concerned with the investigation of the massless regime of an integrable spin chain based on the quantum group deformation of the OSp(3|2) 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 Z(2) degrees of freedom. This view is supported by the fact that the S=1 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.
Highlights
The interest in the study of one-dimensional spin chains goes back at least to the exact solution found by Bethe for the eigenspectrum of the spin-1/2 isotropic Heisenberg model [1]
Recently it was found that the isotropic spin chains invariant by the OSp(n|2m) superalgebra have a number of states in the eigenspectrum leading to the same conformal dimension [6,7]
In this paper we investigate a spin chain which can be derived from a vertex model based on the quantum deformation of the vector representation of the Lie superalgebra OSp(3|2)
Summary
The interest in the study of one-dimensional spin chains goes back at least to the exact solution found by Bethe for the eigenspectrum of the spin-1/2 isotropic Heisenberg model [1]. In this paper we initiate an investigation of the critical behaviour of a spin chain derived from a vertex model based on the quantum superalgebra Uq[OSp(3|2)] This superspin chain has the peculiar feature of having one state whose energy per site has no finite-size correction for arbitrary values of the deformation parameter q in the critical region. This property is probably related to the fact that the R-matrix of this vertex model can be expressed in terms of the generators of a braid-monoid algebra introduced by Birman, Wenzel and Murakami [18,19]. The analysis of the subleading finite-size corrections suggest that for some states we have a combination of power law and logarithmic behaviour
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