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

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

1998-05-20

arxiv.org/abs/cond-mat/9805241v1

Nucl.Phys. B528 (1998) 683-700

Physics

Condensed Matter

Statistical Mechanics

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

Scientific paper

10.1016/S0550-3213(98)00435-0

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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