Constructing the Generalized Gibbs Ensemble after a Quantum Quench

Caux, Jean-Sébastien; Konik, Robert

doi:10.1103/physrevlett.109.175301

Cited by 231 publications

(297 citation statements)

References 39 publications

Supporting

Mentioning

291

Contrasting

Order By: Relevance

“…An explicit solution can then be obtained using the generalized TBA [6,17]. Putting everything together leads to a much simpler expression for the full time evolution (5) …”

Section: Quench Action Approachmentioning

confidence: 99%

“…Though extremely appealing, the implementation of the GGE poses serious challenges, among which is the fact that for many models conservation laws are difficult to handle; calculating the generalized effective temperatures is usually impossible (though exceptional cases where such calculations can be carried through exist [5][6][7]). The GGE was thus mostly implemented for theories which are mappable to free systems, for which the momentum occupation modes can be used as conserved charges [3,4,8].…”

Section: Introductionmentioning

confidence: 99%

“…This scheme, which is based on a generalized thermodynamic Bethe ansatz (TBA) [6,17], is a thermodynamically exact variational method using as input the overlaps * j.denardis@uva.nl of the initial state with the eigenfunctions of the Hamiltonian driving the postquench time evolution. We refer to it as the "quench action" approach; it was up to now only tested on free systems for which independent results were available.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

et al. 2014

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…An explicit solution can then be obtained using the generalized TBA [6,17]. Putting everything together leads to a much simpler expression for the full time evolution (5) …”

Section: Quench Action Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

et al. 2014

Self Cite

View full text Add to dashboard Cite

show abstract

“…A finite-size scaling analysis [65] of expectation values in energy eigenstates of the LL model indicated that the eigenstate thermalization hypothesis [66][67][68] holds for this model in the weak sense [69] only, implying the absence of thermalization following a quench. A recently proposed generalization of the thermodynamic Bethe ansatz (TBA) [70,71] was used in Ref. [72] to obtain the predictions of the nonthermal generalized Gibbs ensemble (GGE) [18,73] for the relaxed state following an interaction-strength quench.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2015

View full text Add to dashboard Cite

We investigate the relaxation dynamics of the integrable Lieb-Liniger model of contact-interacting bosons in one dimension following a sudden quench of the collisional interaction strength. The system is initially prepared in its noninteracting ground state and the interaction strength is then abruptly switched to a positive value, corresponding to repulsive interactions between the bosons. We calculate equal-time correlation functions of the nonequilibrium Bose field for small systems of up to five particles via symbolic evaluation of coordinate Bethe-ansatz expressions for operator matrix elements between Lieb-Liniger eigenstates. We characterize the relaxation of the system by comparing the time-evolving correlation functions following the quench to the equilibrium correlations predicted by the diagonal ensemble and relate the behavior of these correlations to that of the quantum fidelity between the many-body wave function and the initial state of the system. Our results for the asymptotic scaling of local second-order correlations with increasing interaction strength agree with the predictions of recent generalized thermodynamic Bethe-ansatz calculations. By contrast, third-order correlations obtained within our approach exhibit a markedly different power-law dependence on the interaction strength as the Tonks-Girardeau limit of infinitely strong interactions is approached.

show abstract

“…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.…”

Section: Some Results About Interacting Integrable Systemsmentioning

confidence: 99%

Non-equilibrium dynamics of isolated quantum systems

Calabrese

2015

EPJ Web of Conferences

View full text Add to dashboard Cite

Abstract. The non-equilibrium dynamics of isolated quantum systems represent a theoretical and experimental challenge raising many fundamental questions with applications to different fields of modern physics. In these proceedings, we briefly review some of the recent findings on the subject, with particular emphasis to the existence of stationary expectation values of local observables and to their statistical mechanics description. It turns out that the appropriate statistical ensemble describing these asymptotic values depends on whether the Hamiltonian governing the time evolution is integrable or not.

show abstract

Constructing the Generalized Gibbs Ensemble after a Quantum Quench

Cited by 231 publications

References 39 publications

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

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

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

Non-equilibrium dynamics of isolated quantum systems

Contact Info

Product

Resources

About