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

J. Suzuki
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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.

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BibTeXRIS

J. Suzuki. 1998-05-20. Quantum Jacobi-Trudi Formula and $E_8$ Structure in the Ising Model in a Field. https://doi.org/10.1016/s0550-3213(98)00435-0

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