Hidden E-Type Structures in Dilute A Models

The hidden E 7 (E 6) structure has been conjectured for the minimal model \({{\mathcal{M}}_{{4.5}}}({{\mathcal{M}}_{{6.7}}})\) perturbed by Φ1.2 in the context of conformal field theory (CFT). Motivated by this, we examine the dilute A4.6 models, which are expected to be corresponding lattice models. Thermodynamics of the equivalent one-dimensional quantum systems is analyzed via the quantum transfer matrix approach. Appropriate auxiliary functions, related to kinks in the theory, play a role in constructing functional relations among transfer matrices. We successfully recover the universal Y-systems and thereby the thermodynamic Bethe ansatz equations for E 6.7 from the dilute A 6.4 model, respectively.