Inversion identities for inhomogeneous face models

We derive exact inversion identities satisfied by the transfer matrix of inhomogeneous interaction-round-a-face (IRF) models with arbitrary boundary conditions using the underlying integrable structure and crossing properties of the local Boltzmann weights. For the critical restricted solid-on-solid (RSOS) models these identities together with some information on the analytical properties of the transfer matrix determine the spectrum completely and allow to derive the Bethe equations for both periodic and general open boundary conditions.Comment: Latex, 20 page

A generalized spin ladder in a magnetic field

We study the phase diagram of coupled spin-1/2 chains with bilinear and (chiral) three-spin exchange interactions in a magnetic field. The model is soluble on a one-parametric line in the space of coupling constants connecting the limiting cases of a single and two decoupled Heisenberg chains with nearest neighbour exchange only. We give a complete classification of the low-energy properties of the integrable system and introduce a numerical method which allows to study the possible phases of spin ladder systems away from the soluble line in a magnetic field.Comment: Latex2e, 13 pp., 5 figure

The D(D3)D(D_{3})-anyon chain: integrable boundary conditions and excitation spectra

Chains of interacting non-Abelian anyons with local interactions invariant under the action of the Drinfeld double of the dihedral group $D_3$ are constructed. Formulated as a spin chain the Hamiltonians are generated from commuting transfer matrices of an integrable vertex model for periodic and braided as well as open boundaries. A different anyonic model with the same local Hamiltonian is obtained within the fusion path formulation. This model is shown to be related to an integrable fusion interaction round the face model. Bulk and surface properties of the anyon chain are computed from the Bethe equations for the spin chain. The low energy effective theories and operator content of the models (in both the spin chain and fusion path formulation) are identified from analytical and numerical studies of the finite size spectra. For all boundary conditions considered the continuum theory is found to be a product of two conformal field theories. Depending on the coupling constants the factors can be a $Z_4$ parafermion or a $\mathcal{M}_{(5,6)}$ minimal model.Comment: Major revisions have been mad

Correlation functions in the Calogero-Sutherland model with open boundaries

Calogero-Sutherland models of type $BC_N$ are known to be relevant to the physics of one-dimensional quantum impurity effects. Here we represent certain correlation functions of these models in terms of generalized hypergeometric functions. Their asymptotic behaviour supports the predictions of (boundary) conformal field theory for the orthogonality catastrophy and Friedel oscillations.Comment: LaTeX, 11 pages, 1 eps-figur

Finite-size effects in the spectrum of the OSp(3∣2)OSp(3|2) superspin chain

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.Comment: 26 pages, 10 figure

Integrable anyon chains: from fusion rules to face models to effective field theories

Starting from the fusion rules for the algebra $SO(5)_2$ we construct one-dimensional lattice models of interacting anyons with commuting transfer matrices of `interactions round the face' (IRF) type. The conserved topological charges of the anyon chain are recovered from the transfer matrices in the limit of large spectral parameter. The properties of the models in the thermodynamic limit and the low energy excitations are studied using Bethe ansatz methods. Two of the anyon models are critical at zero temperature. From the analysis of the finite size spectrum we find that they are effectively described by rational conformal field theories invariant under extensions of the Virasoro algebra, namely $\mathcal{W}B_2$ and $\mathcal{W}D_5$, respectively. The latter contains primaries with half and quarter spin. The modular partition function and fusion rules are derived and found to be consistent with the results for the lattice model.Comment: 43 pages, published versio