In integrable many-particle systems, it is widely believed that the stationary state reached at late times after a quantum quench can be described by a generalized Gibbs ensemble (GGE) constructed from their extensive number of conserved charges. A crucial issue is then to identify a complete set of these charges, enabling the GGE to provide exact steady-state predictions. Here we solve this long-standing problem for the case of the spin-1=2 Heisenberg chain by explicitly constructing a GGE which uniquely fixes the macrostate describing the stationary behavior after a general quantum quench. A crucial ingredient in our method, which readily generalizes to other integrable models, are recently discovered quasilocal charges. As a test, we reproduce the exact postquench steady state of the Néel quench problem obtained previously by means of the Quench Action method. Introduction.-Understanding and describing the equilibration of isolated many-particle systems is one of the main current challenges of quantum physics. The presence of higher conserved charges (above the Hamiltonian) is linked to the absence of full relaxation to a thermalized state; the conjectured appropriate framework to characterize the steady-state properties in such a situation is the generalized Gibbs ensemble (GGE) [1], in which all available charges are ascribed an individual "chemical potential" set by the initial conditions, and the steady state is the maximal entropy state fulfilling all the constraints associated to the conserved charges . The basic idea underlying the GGE is as follows. Let H ≃ H ð1Þ be the Hamiltonian of an integrable model, and fH ðnÞ g a set of conserved charges fulfilling ½H ðnÞ ; H ðmÞ ¼ 0. The situation we are interested in is that of a quantum quench, where we initially prepare our system in the ground state jΨð0Þi of a local Hamiltonian H 0 and then consider unitary time evolution with respect to our integrable Hamiltonian

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.

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 quenches in integrable spin-1=2 chains in which we evolve the ground state of the antiferromagnetic Ising model with the anisotropic Heisenberg Hamiltonian. For this nontrivially interacting situation, an application of the first-principles-based quench-action method allows us to give an exact description of the postquench steady state in the thermodynamic limit. We show that a generalized Gibbs ensemble, implemented using all known local conserved charges, fails to reproduce the exact quench-action steady state and to correctly predict postquench equilibrium expectation values of physical observables. This is supported by numerical linked-cluster calculations within the diagonal ensemble in the thermodynamic limit. [6] all the way to atomic-scale isolated quantum systems [7]. Much recent experimental and theoretical activity has been focused on the latter, raising fundamental questions as to whether, how, and to what state such systems relax under unitary time evolution following a sudden quantum quench . From this work, two scenarios for equilibration have emerged, one applicable to models having only a few local conserved quantities, the other relevant to integrable models characterized by an infinite number of local conserved charges. In the former, thermalization to a Gibbs ensemble is the rule [11], while in the latter, equilibration to a so-called generalized Gibbs ensemble (GGE) [9,10] is generally thought to occur, in particular for lattice spin systems [12][13][14][15][16][17][18][19][20].In this Letter, we study a quench in which the second scenario breaks down. Our initial state, defined as a purely antiferromagnetic (spin-1=2 Néel) state, is let to evolve unitarily in time according to the XXZ spin chain Hamiltonian. This is a physically meaningful quench protocol, which can, in principle, be implemented using cold atoms [43][44][45][46][47]. We provide a thermodynamically exact solution for the steady state reached long after the quench, derived directly from microscopics using the recently proposed quench-action method [48]. The solution takes the form of a set of distributions of quasimomenta that completely characterizes the macrostate representing the steady state, from which observables ...

Abstract. We derive a determinant expression for overlaps of Bethe states of the XXZ spin chain with the Néel state, the ground state of the system in the antiferromagnetic Ising limit. Our formula, of determinant form, is valid for generic system size. Interestingly, it is remarkably similar to the well-known Gaudin formula for the norm of Bethe states, and to another recently-derived overlap formula appearing in the Lieb-Liniger model.

The steady state after a quantum quench from the Néel state to the anisotropic Heisenberg model for spin chains is investigated. Two methods that aim to describe the postquench non-thermal equilibrium, the generalized Gibbs ensemble and the quench action approach, are discussed and contrasted. Using the recent implementation of the quench action approach for this Néel-to-XXZ quench, we obtain an exact description of the steady state in terms of Bethe root densities, for which we give explicit analytical expressions.Furthermore, by developing a systematic small-quench expansion around the antiferromagnetic Ising limit, we analytically investigate the differences between the predictions of the two methods in terms of densities and postquench equilibrium expectation values of local physical observables. Finally, we discuss the details of the quench action solution for the quench to the isotropic Heisenberg spin chain. For this case we validate the underlying assumptions of the quench action approach by studying the large-system-size behavior of the overlaps between Bethe states and the Néel state.

Abstract. We specialize a recently-proposed determinant formula [1] for the overlap of the zero-momentum Néel state with Bethe states of the spin-1/2 XXZ chain to the case of an odd number of downturned spins, showing that it is still of "Gaudin-like" form, similar to the case of an even number of down spins. We generalize this result to the overlap of q-raised Néel states with parity-invariant Bethe states lying in a nonzero magnetization sector. The generalized determinant expression can then be used to derive the corresponding determinants and their prefactors in the scaling limit to the Lieb-Liniger (LL) Bose gas. The odd number of down spins directly translates to an odd number of bosons.We furthermore give a proof that the Néel state has no overlap with non-parityinvariant Bethe states. This is based on a determinant expression for overlaps with general Bethe states that was obtained in the context of the XXZ chain with open boundary conditions [2][3][4]. The statement that overlaps with non-parity-invariant Bethe states vanish is still valid in the scaling limit to LL which means that the BEC state [5] has zero overlap with non-parity-invariant LL Bethe states.

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