Interaction quenches in the one-dimensional Bose gas

Abstract

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. The nonequilibrium dynamics of integrable systems are highly constrained by the conservation of certain charges. There is substantial evidence that after a quantum quench they do not thermalize but their asymptotic steady state can be described by a generalized Gibbs ensemble (GGE) built from the conserved charges. Most of the studies on the GGE so far have focused on models that can be mapped to quadratic systems, while analytic treatment in nonquadratic systems remained elusive. We obtain results on interaction quenches in a nonquadratic continuum system, the one-dimensional (1D) Bose gas described by the integrable Lieb-Liniger model. The direct implementation of the GGE prescription is prohibited by the divergence of the conserved charges, which we conjecture to be endemic to any continuum integrable systems with contact interactions undergoing a sudden quench. We compute local correlators for a noninteracting initial state and arbitrary final interactions as well as two-point functions for quenches to the Tonks-Girardeau regime. We show that in the long time limit integrability leads to significant deviations from the predictions of the grand canonical ensemble, allowing for an experimental verification in cold-atom systems.

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

“…Besides being of experimental interest [13][14][15], this case, surprisingly, cannot be treated theoretically using the standard GGE, due to creeping infinities in the expectation values of the conserved charges [12].…”

“…In this paper, we deal with a specific quench problem of recent interest [9][10][11][12], namely the interaction quench in the Lieb-Liniger (LL) Bose gas and more specifically the release of the noninteracting Bose-Einstein condensate (BEC) ground state into a system with finite repulsive interactions. Besides being of experimental interest [13][14][15], this case, surprisingly, cannot be treated theoretically using the standard GGE, due to creeping infinities in the expectation values of the conserved charges [12].…”

Non-equilibrium dynamics of isolated quantum systems

“…an exact knowledge of the spectrum and of the eigenstates, but not often in a very practical form) and although a few methods have been developed specifically to tackle these out of equilibrium problems [48][49][50][51][52]. Due to these difficulties, many studies attempted the explicit exact construction of the GGE [53][54][55] starting from specific initial conditions. These GGE predictions could be (and have been in some cases) successively tested in numerical simulations or even in actual experiments.…”

“…c = 0) has been firstly studied in Ref. [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.…”

Universal postquench coarsening and aging at a quantum critical point

“…It is in general difficult to make quantitative predictions for the non-equilibrium dynamics of interacting quantum many-body systems beyond the mean-field approximation 34 -except in cases where exact solutions are available [35][36][37][38][39][40][41][42][43][44][45] or when controlled numerical approaches are established such as for impurity models [46][47][48][49][50][51][52][53] and for one-dimensional systems 22,[54][55][56][57][58][59][60][61][62] . Here, we exploit the presence of a quantum critical point to analytically solve for the universal dynamics of an interacting quantum ϕ 4 -model, which is an effective description of a number of experimental systems 63 .…”