Solution for an interaction quench in the Lieb-Liniger Bose gas

Abstract

Solution for an interaction quench in the Lieb-Liniger Bose gasDe Nardis, J.; Wouters, B.M.; Brockmann, M.; Caux, J.S. General rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: http://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. We study a quench protocol where the ground state of a free many-particle bosonic theory in one dimension is let unitarily evolve in time under the integrable Lieb-Liniger Hamiltonian of δ-interacting repulsive bosons. By using a recently proposed variational method, we here obtain the exact nonthermal steady state of the system in the thermodynamic limit and discuss some of its main physical properties. Besides being a rare case of a thermodynamically exact solution to a truly interacting quench situation, this interestingly represents an example where a standard implementation of the generalized Gibbs ensemble fails.

Relaxation dynamics of the Lieb-Liniger gas following an interaction quench: A coordinate Bethe-ansatz analysis

“…This generalized TBA also forms the basis for the so-called quench-action variational approach [74,75], which was used in Ref. [76] to predict the dynamical evolution of correlation functions following such a quench. We note also studies of related nonequilibrium scenarios such as a quench to the so-called super-Tonks regime [77,78] of strong attractive interactions [79,80] and a coherent splitting [12] of the LL gas [81].…”

“…Moreover, our results for second-order correlations in the DE corroborate the predictions of Refs. [72,76] for the generalized equilibrium state of the system. In particular, our DE results for local second-order correlations are consistent with the power-law scaling with interaction strength predicted by Refs.…”

Non-equilibrium dynamics of isolated quantum systems

“…[53] where the GGE was approximately constructed with an ingenious integrable lattice regularisation of the model. Subsequently the overlaps have been analytically derived [63], allowing (thanks to the quench action method of Ref. [52]) the explicit evaluation of the long time limit of many observables [63] whose values agree with the previously constructed GGE.…”

“…Subsequently the overlaps have been analytically derived [63], allowing (thanks to the quench action method of Ref. [52]) the explicit evaluation of the long time limit of many observables [63] whose values agree with the previously constructed GGE. It is worth mentioning that the quench from c = 0 to c = ∞ has been treated with more elementary techniques [46], whose results are reproduced by the proper limit of the general construction [63].…”

“…What is not (yet) known in general is how to obtain the overlaps between Bethe states and generic initial states. Up to now, only very few exact results exist for these overlaps with very specific initial states [57][58][59][60][61][62][63]. Clearly, finding compact and tractable expressions for the overlaps between Bethe states and more generic initial states would allow exact calculations for a variety of potentially interesting situations and experiments.…”