# SciPost Thesis Link

Title: | Correlation functions of in- and out-of-equilibrium integrable models | |

Author: | J. De Nardis | |

As Contributor: | (not claimed) | |

Type: | Ph.D. | |

Discipline: | Physics | |

Subject area: | Condensed Matter Physics - Theory | |

Approach: | Theoretical | |

URL: | http://hdl.handle.net/11245/1.485898 | |

Degree granting institution: | University of Amsterdam | |

Supervisor(s): | J.-S. Caux | |

Defense date: | 2015-09-25 |

### Abstract:

The main purpose of this thesis is to present an exact computation of the one or two-points correlation functions of integrable models (in particular the Lieb- Liniger model [22] and the XXZ spin chain [98–100]) in equilibrium and non equilibrium conditions and for large system sizes (thermodynamic limit). This is done rst by introducing the fundamental tools of the coordinate and alge- braic Bethe ansatz in chapter 2 which allows to obtain the exact eigenfuntions and scalar products between them. In this chapter we also address the question of how to determine when a quantum model is integrable or not, following the work of Jorn Mossel [101, 102]. Then in chapter 3 we move to the problem of computing overlaps between eigenstates of di erent models. This has a direct application to quench problems and until now it has been poorly addressed in the eld of integrable systems. Chapter 4 is devoted to an extensive treatment of the thermodynamic limit of integrable models. In particular we focus on the idea of thermodynamic Bethe states, namely how to characterize them and how to de ne the matrix elements between them, starting from their nite size expres- sions. Here we obtain some results for equilibrium nite temperature correlation functions in the one-dimensional Bose gas, which represent a direct extension of the work initiated in Miłosz Pan l’s thesis [103]. Thereafter we concentrate on the out-of-equilibrium aspects of the Lieb-Liniger model in chapter 5 focus- ing in particular on the quench from the ground state of the free bosonic theory (BEC state) to the fully interacting system. The corresponding post-quench time evolution of weak observables, computed via the quench action method, is addressed in chapter 6. Finally chapter 7 analyzes the quench from the Néel initial state to the XXZ spin chain. This quench reveals unknown results on the con- served quantities of the model, underlining the role of quasi-local operators to reconstruct the equilibrium steady-state values of local operators even when the spectrum of the Hamiltonian is gapped.