This paper is concerned with the investigation of the massless regime of an integrable spin chain based on the quantum group deformation of the O S p ( 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.
The thermodynamic limit of superspin chains can show several intriguing properties, including the emergence of continua of scaling dimensions and the appearance of discrete states when imposing toroidal boundary conditions. Nevertheless, the former’s exhaustive characterization in terms of Conformal Field Theories is still lacking. In order to study the thermodynamic limit of the U_q[sl(2|1)] 3 ⊗ 3̄ superspin chain in the antiferromagnetic regime, we analyze the low lying excitations by means of the model’s exact solution using the Algebraic Bethe Ansatz. In the isotropic limit, this model may be used as a toy model for the description of plateau transitions in Quantum Hall systems. The definition of a quasimomentum operator allows for a characterization of the continua of scaling dimensions, thereby giving rise to a quantum number for the corresponding non-compact component of the spectrum in the thermodynamic limit. The associated degeneracies are lifted on the lattice by logarithmic fine structures. Based on the extrapolation of our finite size data we find that under a variation of the boundary conditions from periodic to antiperiodic for the fermionic degrees of freedom, levels from the continuous part of the spectrum flow into discrete levels and vice versa. Investigating the thermodynamic limit of the q-deformed osp(3|2) superspin chain, corresponding to an intersecting loop model in the rational limit, we seek to uncover its low-lying critical exponents. We present evidences that the latter are built in terms of composites of anomalous dimensions of two Coulomb gases with distinct radii and 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 the 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 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.
In this paper we investigate the spectrum of OSp(n|2m) quantum spin chains with free boundary conditions. We compute the surface free energy of these models which, similar to other properties in the thermodynamic limit including the effective central charge of the underlying conformal field theory, depends on n−2m only. For several models in the regime n−2m<2 we have studied the finite-size properties including the subleading logarithmic corrections to scaling. As in the case of periodic boundary conditions we find the existence of a tower of states with the same conformal dimension as the identity operator. As expected the amplitudes of the corresponding logarithmic corrections differ from those found previously for the models with periodic boundary conditions. We point out however the existence of simple relations connecting such amplitudes for free and periodic boundaries. Based on our findings we formulate a conjecture on the long distance behaviour of the bulk and surface watermelon correlators.
The low energy spectrum of a spin chain with OSp(3|2) 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 z=1 which provides a framework to study the critical properties of the unusual low temperature Goldstone phase of the O(N) sigma model for N=1 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 OSp(3|2). 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.
We present the finite-size scaling theory of one-dimensional quantum critical systems in the presence of boundaries. While the finite-size spectrum in the conformal limit, namely of a conformal field theory with conformally invariant boundary conditions, is related to the dimensions of boundary operators by Cardy, the actual spectra of lattice models are affected by both bulk and boundary perturbations and contain non-universal boundary energies. We obtain a general expression of the finite-size energy levels in the presence of bulk and boundary perturbations. In particular, a generic boundary perturbation related to the energy-momentum tensor gives rise to a renormalization of the effective system size. We verify our field-theory formulation by comparing the results with the exact solution of the critical transverse-field Ising chain and with accurate numerical results on the critical three-state Potts chain obtained by Density-Matrix Renormalization Group.
A bstract We consider the quantum integrable spin chain models associated with the Jimbo R-matrix based on the quantum affine algebra
Dn+1(2) D n + 1 2 , subject to quantum-group-invariant boundary conditions parameterized by two discrete variables p = 0, . . . , n and ε = 0, 1. We develop the analytical Bethe ansatz for the previously unexplored case ε = 1 with any n , and use it to investigate the effects of different boundary conditions on the finite-size spectrum of the quantum spin chain based on the rank-2 algebra
D3(2) D 3 2 . Previous work on this model with periodic boundary conditions has shown that it is critical for the range of anisotropy parameters 0 < γ < π /4, where its scaling limit is described by a non-compact CFT with continuous degrees of freedom related to two copies of the 2D black hole sigma model. The scaling limit of the model with quantum-group-invariant boundary conditions depends on the parameter ε : similarly as in the rank-1
D2(2) D 2 2 chain, we find that the symmetry of the lattice model is spontaneously broken, and the spectrum of conformal weights has both discrete and continuous components, for ε = 1. For p = 1, the latter coincides with that of the
D2(2) D 2 2 chain, which should correspond to a non-compact brane related to one black hole CFT in the presence of boundaries. For ε = 0, the spectrum of conformal weights is purely discrete.