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 subleading 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 oneparticle 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 offcritical 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.
JeanSébastien 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], quasionedimensional cold atom gases were observed with unprecedented accuracy, providing impetus for many developments on the effects of low dimensionality in outofequilibrium 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 phasespace 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 manybody dephasing. We also analyze the effects of weak anharmonicity. In the experiment, measurements are made after release from the onedimensional trap. We evaluate the gas density curves after such a release, characterizing the actual time necessary for reaching the asymptotic state where the integrable quasiparticle 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 nonthermal excited states with unusual properties. The most common way to probe them is by performing a quantum quench, i.e., by letting a manybody 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 fluctuationdissipation theorem that we provide. Our procedure allows us to completely reconstruct the stationary state of a quantum integrable system from stateoftheart experimental observations.