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Title:  Quantum integrable models out of equilibrium
Author:  J.J. Mossel
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:  2012-09-13


Outline In the next two chapters we introduce the most important tool used in this thesis, the Bethe ansatz. We start chapter 2 with a discussion of what wavefunctions in one dimension might look like, followed by the so-called coordinate Bethe ansatz for wavefunctions of the Lieb-Liniger model and the XXZ spin chain. Although the coordinate Bethe ansatz is quite useful for gaining an intuitive understanding, for actually computing correlation functions and for studying quench problems we need the algebraic Bethe ansatz presented in 3. In chapter 4, we discuss the notion of quantum integrability and introduce a new definition, leading to a clas- sification of integrable models [52]. We change gears in the following two chapters by studying the time evolution after two types of quantum quenches. Chapter 5 deals with the problem of a spin chain, initially prepared in a spatially inhomo- geneous (domain wall) state, where subsequent time evolution is governed by the XXZ chain [53]. In chapter 6, we study the case where the system is initially in the ground state of the fully interacting Lieb-Liniger model. The quench consists of instantaneously switching the interactions off [54]. A more formal discussion of equilibrium states (e.g. the large time limit after a quantum quench) is presented in chapter 7 where we introduce the generalized thermodynamic Bethe ansatz [55]. We end with a conclusion of our results and discuss possible directions for future research.

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