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.

arXiv comment16 pages +Table, 4 Figures, Latex 2e, use graphicx

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• Magnetic Correlation Length and Universal Amplitude of the Lattice E_8 Ising Model
• Fusion of Dilute $A_L$ Lattice Models
• Scaling Limit of the Ising Model in a Field
• Fusion $U_q(G_2^{(1)})$ vertex models and analytic Bethe ans{ä}tze
• An Ising model in a magnetic field with a boundary
• Single Particle Excitations in the Lattice E_8 Ising Model

Cited by in corpus (13)

• Spinons in Magnetic Chains of Arbitrary Spins at Finite Temperatures
• Functional Relations in Stokes Multipliers and Solvable Models related to U_q(A^{(1)}_n)
• Commuting quantum transfer matrix approach to intrinsic Fermion system: Correlation length of a spinless Fermion model
• Free Field Approach to the Dilute A_L Models
• Integrable aspects of the scaling q-state Potts models II: finite-size effects
• Thermodynamic Bethe ansatz equation from fusion hierarchy of osp(1|2) integrable spin chain
• Excited state TBA and functional relations in spinless Fermion model
• The inversion relation and the dilute A_{3,4,6} eigenspectrum
• T-W relation and free energy of the Heisenberg chain at a finite temperature
• Critical site percolation on the triangular lattice: From integrability to conformal partition functions
• The dilute A${}_4$ model, the E${}_7$ mass spectrum and the tricritical Ising model
• The dilute A_L models and the integrable perturbations of unitary minimal CFTs
• The dilute A_L models and the Phi_{1,2} perturbation of unitary minimal CFTs