We derive a generalization of the Destri -De Vega equation governing the scaling functions of some excited states in the Sine-Gordon theory. In particular configurations with an even number of holes and no strings are analyzed and their UV limits found to match some of the conformal dimensions of the corresponding compactified massless free boson. Quantum group reduction allows to interpret some of our results as scaling functions of excited states of Restricted Sine-Gordon theory, i.e. minimal models perturbed by φ 13 in their massive regime. In particular we are able to reconstruct the scaling functions of the off-critical deformations of all the scalar primary states on the diagonal of the Kac-table.

We prove a useful identity valid for all ADE minimal S-matrices, that clarifies the transformation of the relative thermodynamic Bethe Ansatz (TBA) from its standard form into the universal one proposed by Al.B.Zamolodchikov.By considering the graph encoding of the system of functional equations for the exponentials of the pseudoenergies, we show that any such system having the same form as those for the ADE TBA's, can be encoded on A, D, E, A/Z 2 only. This includes, besides the known ADE diagonal scattering, the set of all SU (2) related magnonic TBA's. We explore this class sistematically and find some interesting new massive and massless RG flows. The generalization to classes related to higher rank algebras is briefly presented and an intriguing relation with level-rank duality is signalled. *

A Bethe Ansatz solution of the open spin-1 2 XXZ quantum spin chain with nondiagonal boundary terms has recently been proposed. Using a numerical procedure developed by McCoy et al., we find significant evidence that this solution can yield the complete set of eigenvalues for generic values of the bulk and boundary parameters satisfying one linear relation. Moreover, our results suggest that this solution is practical for investigating the ground state of this model in the thermodynamic limit.

In this letter we show that the Rényi entanglement entropy of a region of large size in a one-dimensional critical model whose ground state breaks conformal invariance (such as in those described by non-unitary conformal field theories), behaves as S n ∼ c eff (n+1) 6n log , where c eff = c − 24∆ > 0 is the effective central charge, c (which may be negative) is the central charge of the conformal field theory and ∆ = 0 is the lowest holomorphic conformal dimension in the theory. We also obtain results for models with boundaries, and with a large but finite correlation length, and we show that if the lowest conformal eigenspace is logarithmic (L 0 = ∆I +N with N nilpotent), then there is an additional term proportional to log(log ). These results generalize the well known expressions for unitary models. We provide a general proof, and report on numerical evidence for a non-unitary spin chain and an analytical computation using the corner transfer matrix method for a non-unitary lattice model. We use a new algebraic technique for studying the branching that arises within the replica approach, and find a new expression for the entanglement entropy in terms of correlation functions of twist fields for non-unitary models.