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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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.
Giuseppe Del Vecchio Del Vecchio, Alvise Bastianello, Andrea De Luca, Giuseppe Mussardo
SciPost Phys. 9, 002 (2020) ·
published 6 July 2020
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We study the out-of-equilibrium properties of a classical integrable
non-relativistic theory, with a time evolution initially prepared with a finite
energy density in the thermodynamic limit. The theory considered here is the
Non-Linear Schrodinger equation which describes the dynamics of the
one-dimensional interacting Bose gas in the regime of high occupation numbers.
The main emphasis is on the determination of the late-time Generalised Gibbs
Ensemble (GGE), which can be efficiently semi-numerically computed on arbitrary
initial states, completely solving the famous quench problem in the classical
regime. We take advantage of known results in the quantum model and the
semiclassical limit to achieve new exact results for the momenta of the density
operator on arbitrary GGEs, which we successfully compare with ab-initio
numerical simulations. Furthermore, we determine the whole probability
distribution of the density operator (full counting statistics), whose exact
expression is still out of reach in the quantum model.
