The spectrum properties of an integrable $G_2$ invariant vertex model

DOI10.1016/J.NUCLPHYSB.2023.116131arXiv2301.05963MaRDI QIDQ6423407

Publication date: 14 January 2023

Abstract: This paper is concerned with the study of properties of the exact solution of the fundamental integrable

G_{2}

vertex model. The model

R

-matrix and respective spin chain are presented in terms of the basis generators of the

G_{2}

Lie algebra. This formulation permits us to related the number of the Bethe roots of the respective Bethe equations with the eigenvalues of the

U (1)

conserved charges from the Cartan subalgebra of

G_{2}

. The Bethe equations are solved by a peculiar string structure which combines complex three-strings with real roots allowing us determine the bulk properties in the thermodynamic limit. We argue that

G_{2}

spin chain is gapless but the low-lying excitations have two different speeds of sound and the underlying continuum limit is therefore not strictly Lorentz invariant. We have investigate the finite-size corrections to the ground state energy and proposed that the critical properties of the system should be governed by the product of two

c = 1

conformal field theories. By combining numerical and analytical methods we have computed the bulk free-energy of the

G_{2}

vertex model. We found that there are three regimes in the spectral parameter in which the free-energy is limited and continuous. There exists however at least two sharp corner points in which the bulk-free energy is not differentiable.

Mathematics Subject Classification ID

Statistical thermodynamics (82B30)

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