Axel Cortés Cubero, Robert M. Konik, Máté Lencsés, Giuseppe Mussardo, Gabor Takács
SciPost Phys. 12, 162 (2022) ·
published 16 May 2022
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· pdf
The thermal deformation of the critical point action of the 2D tricritical
Ising model gives rise to an exact scattering theory with seven massive
excitations based on the exceptional $E_7$ Lie algebra. The high and low
temperature phases of this model are related by duality. This duality
guarantees that the leading and sub-leading magnetisation operators,
$\sigma(x)$ and $\sigma'(x)$, in either phase are accompanied by associated
disorder operators, $\mu(x)$ and $\mu'(x)$. Working specifically in the high
temperature phase, we write down the sets of bootstrap equations for these four
operators. For $\sigma(x)$ and $\sigma'(x)$, the equations are identical in
form and are parameterised by the values of the one-particle form factors of
the two lightest $\mathbb{Z}_2$ odd particles. Similarly, the equations for
$\mu(x)$ and $\mu'(x)$ have identical form and are parameterised by two
elementary form factors. Using the clustering property, we show that these four
sets of solutions are eventually not independent; instead, the parameters of
the solutions for $\sigma(x)/\sigma'(x)$ are fixed in terms of those for
$\mu(x)/\mu'(x)$. We use the truncated conformal space approach to confirm
numerically the derived expressions of the matrix elements as well as the
validity of the $\Delta$-sum rule as applied to the off-critical correlators.
We employ the derived form factors of the order and disorder operators to
compute the exact dynamical structure factors of the theory, a set of
quantities with a rich spectroscopy which may be directly tested in future
inelastic neutron or Raman scattering experiments.
