We consider the non-equilibrium dynamics in quantum field theories (QFTs). After being prepared in a density matrix that is not an eigenstate of the Hamiltonian, such systems are expected to relax locally to a stationary state. In presence of local conservation laws, these stationary states are believed to be described by appropriate generalized Gibbs ensembles. Here we demonstrate that in order to obtain a correct description of the stationary state, it is necessary to take into account conservation laws that are not (ultra-)local in the usual sense of QFT, but fulfil a significantly weaker form of locality. We discuss implications of our results for integrable QFTs in one spatial dimension. PACS numbers:Introduction. The last decade has witnessed dramatic progress in realizing and analyzing isolated many-particle quantum systems out of equilibrium [1][2][3][4][5][6]. Key questions that emerged from these experiments is why and how observables relax towards time independent values, and what principles underlie a possible statistical description of the latter . It was demonstrated early on that non-equilibrium dynamics is strongly affected by dimensionality, and that conservation laws play an important role. In particular, the experiments of [2] on trapped 87 Rb atoms established that three-dimensional condensates rapidly relax to a stationary state characterized by an effective temperature, whereas constraining the motion of atoms to one dimension greatly reduces the relaxation rate and dramatically changes the nature of the stationary state. The suggestion that this unusual steady state is a consequence of (approximate) conservation laws motivated a host of theoretical studies investigation the role played by conservation laws. We may summarize the results of these works as follows: given an initial state |Ψ and a translationally invariant system with Hamiltonian H ≡ I 0 and conservation laws I n such that [I n , I m ] = 0, the stationary behaviour of n-point functions of local operators O a (x) in the thermodynamic limit is described by a generalized Gibbs ensemble, as proposed by Rigol et al in a seminal paper [9]

Interactions are known to have dramatic effects on bosonic gases in one dimension (1D). Not only does the ground state transform from a condensate like state to an effective Fermi sea, but new fundamental excitations, which do not have any higher-dimensional equivalents, are predicted to appear. In this work, we trace these elusive excitations via their effects on the dynamical structure factor of 1D strongly interacting Bose gases at low temperature. An array of 1D Bose gases is obtained by loading a 87 Rb condensate in a two-dimensional lattice potential. The dynamical structure factor of the system is probed by energy deposition through low-momentum Bragg excitations. The experimental signals are compared to recent theoretical predictions for the dynamical structure factor of the Lieb-Liniger model at T > 0. Our results demonstrate that the main contribution to the spectral widths stems from the dynamics of the interaction-induced excitations in the gas, which cannot be described by the Luttinger liquid theory.

Probing the Excitations of a Lieb-Liniger Gas from Weak to Strong CouplingMeinert, F.; Panfil, M.K.; Mark, M. J.; Lauber, K.; Caux, J.S.; Nägerl, H.-C. 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. Download date: 11 May 2018Probing the Excitations of a Lieb-Liniger Gas from Weak to Strong Coupling We probe the excitation spectrum of an ultracold one-dimensional Bose gas of cesium atoms with a repulsive contact interaction that we tune from the weakly to the strongly interacting regime via a magnetic Feshbach resonance. The dynamical structure factor, experimentally obtained using Bragg spectroscopy, is compared to integrability-based calculations valid at arbitrary interactions and finite temperatures. Our results unequivocally underlie the fact that holelike excitations, which have no counterpart in higher dimensions, actively shape the dynamical response of the gas.

We address the problem of calculating finite-temperature response functions of an experimentally relevant low-dimensional, strongly correlated system: the integrable one-dimensional Bose gas with a repulsive δ-function interaction (the Lieb-Liniger model). Focusing on the dynamical density-density function, we present a Bethe ansatz-based method allowing for its accurate evaluation in finite but large systems, over broad ranges of momenta, frequencies, temperatures, and interaction parameters which are difficult to access using other methods. This allows us to quantify the reshaping of the zero-temperature critical behavior by thermal fluctuations, in experimentally accessible regimes.

Abstract. In this article we demonstrate a recently developed technique which addresses the problem of obtaining non-universal prefactors of the correlation functions of 1D systems at zero temperature. Our approach combines the effective field theory description of generic 1D quantum liquids with the finite size scaling of form factors (matrix elements) which are obtained using microscopic techniques developed in the context of integrable models. We thus establish exact analytic forms for the prefactors of the long-distance behavior of equal time correlation functions as well as prefactors of singularities of dynamic response functions. In this article our focus is on three specific integrable models: the CalogeroSutherland, Lieb-Liniger, and XXZ models.Exact prefactors of correlation functions of 1D quantum integrable models 2

We consider the Lieb-Liniger model for a gas of bosonic δ−interacting particles. Using Algebraic Bethe Ansatz results we compute the thermodynamic limit of the form factors of the density operator between finite entropy eigenstates such as finite temperature states or generic non-equilibrium highly excited states. These form factors are crucial building blocks to obtain the thermodynamic exact dynamic correlation functions of such physically relevant states. As a proof of principle we compute an approximated dynamic structure factor by including only the simplest types of particle-hole excitations and show the agreement with known results. arXiv:1411.4537v4 [cond-mat.quant-gas]

We study the density-density correlation function of the 1D Lieb-Liniger model and obtain an exact expression for the small momentum limit of the static correlator in the thermodynamic limit. We achieve this by summing exactly over the relevant form factors of the density operator in the small momentum limit. The result is valid for any eigenstate, including thermal and non-thermal states. We also show that the small momentum limit of the dynamic structure factors obeys a generalized detailed balance relation valid for any equilibrium state.

We review the recently introduced thermodynamic form factors for pairs of particle-hole excitations on finite-entropy states in the Lieb-Liniger model. We focus on the density operator and we show how the form factors can be used for analytic computations of dynamical correlation functions. We derive a new representation for the form factors and we discuss some aspects of their structure. We rigorously show that in the small momentum limit (or equivalently, on hydrodynamic scales) a single particle-hole excitation fully saturates the spectral sum and we also discuss the contribution from two particle-hole pairs. Finally we show that thermodynamic form factors can be also used to study the ground state correlations and to derive the edge exponents.arXiv:1712.06581v5 [cond-mat.quant-gas] 30 May 2018