Quantum Jacobi-Trudi Formula and $E_8$ Structure in the Ising Model in a Field

Abstract

We investigate a 1D quantum system associated with the Ising model in a field(the dilute $A_3$ 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 Jacobi-Trudi formula, together with special features at "root of unity" . The numerical analysis on their eigenvalues shows a remarkable coincidence with exponents characteristic to $E_8$. From these findings, we have successfully recovered the $E_8$ Thermodynamic Bethe ansatz equation by Bazhanov et al, however, without specific choice of strings solutions.

16 pages +Table, 4 Figures, Latex 2e, use graphicx

References in corpus (2)

• From Fusion Hierarchy to Excited State TBA
• Magnetic Correlation Length and Universal Amplitude of the Lattice E_8 Ising Model

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