Quantum Jacobi-Trudi formula and E8 structure in the Ising model in a field Original Research Article

We investigate a 1D quantum system associated with the Ising model in a field (the dilute A3 model) by the recently developed quantum transfer matrix (QTM) approach. A closed set of functional relations is found among variants of fusion QTMs which are characterized by skew Young tableaux. These relations are proved by using a quantum analogue of the Jacobi-Trudi formula, together with special features at the “root of unity”. The numerical analysis of their eigenvalues shows a remarkable coincidence with exponents characteristic to E8. From these findings, we have successfully recovered the E8 thermodynamic Bethe ansatz equation by Bazhanov et al., however, without a specific choice of strings solutions.