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Title:  The quench action approach to out-of-equilibrium quantum integrable models
Author:  B.M. Wouters
As Contributor:   (not claimed)
Type: Ph.D.
Field: Physics
  • Condensed Matter Physics - Theory
Approach: Theoretical
Degree granting institution:  University of Amsterdam
Supervisor(s): J.-S. Caux
Defense date:  2015-10-02


The outline of this thesis is as follows. In Chapter 2 we give a detailed introduc- tion to the coordinate Bethe Ansatz for the Lieb-Liniger model and the spin-1/2 XXZ spin chain, and a brief review of the algebraic Bethe Ansatz. Special at- tention is given to the thermodynamic limit of the coordinate Bethe Ansatz, as this is essential for a careful derivation of the quench action approach. Readers familiar with Bethe Ansatz techniques can safely skip this chapter. In Chapter 3 we give a technical introduction to global quantum quenches and the generalized Gibbs ensemble. Then, the quench action approach is carefully derived from first principles. We also specify for which initial states and what type of observables the QA method is applicable. An explicit first check of the QA approach in the context of the transverse-field Ising chain, which is mappable to free (Majorana) fermions, is reviewed. The first implementation of the QA approach to a truly interacting inte- grable model is presented in Chapter 4 for a quench from the 1D free-boson gas to the repulsive Lieb-Liniger model. Due to creeping infinities of the local conserved charges the GGE is inapplicable and only the QA approach can solve this quench problem in the thermodynamic limit. Exact overlaps are given, the GTBA equation is derived and analytically solved, and the physical properties of the representative state are discussed. We also compute the postquench time- evolution of the density-density correlator in the Tonks-Girardeau regime. Chapter 5 is devoted to quenches from the N ́eel state to the spin-1/2 XXZ chain in the gapped phase and at the isotropic point. We solve this problem using the QA approach and analyze its solution in great detail. Interestingly, we are also able to perform an exact GGE analysis for these quenches and make (analytical) comparisons between both methods. Modelling the Bragg pulse for the Lieb-Liniger gas in Chapter 6 brings us closer to actual experiments, like the one in Ref. [24]. We apply the quench action logic to instantaneous pulses on the Tonks-Girardeau ground state and use the Fermi-Bose mapping to study long Bragg pulses and pulses in a parabolic trap, for which we identify a pre-thermalization plateau governed by the GGE. In the concluding Chapter 7 we do three things. We summarize the main results of this thesis, we give an overview of other applications of the QA approach to different models than the ones considered here, and we present some pressing open problems (to some of which we also present preliminary solutions) and directions for future research.

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