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.
Jean-Sébastien Caux, Benjamin Doyon, Jérôme Dubail, Robert Konik, Takato Yoshimura
SciPost Phys. 6, 070 (2019) ·
published 20 June 2019
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Describing and understanding the motion of quantum gases out of equilibrium
is one of the most important modern challenges for theorists. In the
groundbreaking Quantum Newton Cradle experiment [Kinoshita, Wenger and Weiss,
Nature 440, 900, 2006], quasi-one-dimensional cold atom gases were observed
with unprecedented accuracy, providing impetus for many developments on the
effects of low dimensionality in out-of-equilibrium physics. But it is only
recently that the theory of generalized hydrodynamics has provided the adequate
tools for a numerically efficient description. Using it, we give a complete
numerical study of the time evolution of an ultracold atomic gas in this setup,
in an interacting parameter regime close to that of the original experiment. We
evaluate the full evolving phase-space distribution of particles. We simulate
oscillations due to the harmonic trap, the collision of clouds without
thermalization, and observe a small elongation of the actual oscillation period
and cloud deformations due to many-body dephasing. We also analyze the effects
of weak anharmonicity. In the experiment, measurements are made after release
from the one-dimensional trap. We evaluate the gas density curves after such a
release, characterizing the actual time necessary for reaching the asymptotic
state where the integrable quasi-particle momentum distribution function
emerges.
Jacopo De Nardis, Miłosz Panfil, Andrea Gambassi, Leticia F. Cugliandolo, Robert Konik, Laura Foini
SciPost Phys. 3, 023 (2017) ·
published 27 September 2017
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Quantum integrable models display a rich variety of non-thermal excited
states with unusual properties. The most common way to probe them is by
performing a quantum quench, i.e., by letting a many-body initial state
unitarily evolve with an integrable Hamiltonian. At late times, these systems
are locally described by a generalized Gibbs ensemble with as many effective
temperatures as their local conserved quantities. The experimental measurement
of this macroscopic number of temperatures remains elusive. Here we show that
they can be obtained by probing the dynamical structure factor of the system
after the quench and by employing a generalized fluctuation-dissipation theorem
that we provide. Our procedure allows us to completely reconstruct the
stationary state of a quantum integrable system from state-of-the-art
experimental observations.
