# SciPost Thesis Link

Title: | A quantum statistical approach to quantum correlations in many-body systems | |

Author: | Irénée Frérot | |

As Contributor: | (not claimed) | |

Type: | Ph.D. | |

Discipline: | Physics | |

Domain: | Theoretical | |

Subject area: | Quantum Physics | |

URL: | https://hal.archives-ouvertes.fr/tel-01679743 | |

Degree granting institution: | Université de Lyon | |

Supervisor(s): | Tommaso Roscilde | |

Defense date: | 2017-10-09 |

### Abstract:

The notion of coherence, intimately related to the notion of wave-particle duality, plays a central role in quantum mechanics. When quantum coherence extends over several particles inside a system, the description in terms of individual objects becomes impossible, due to the development of quantum correlations (or entanglement). In this manuscript, we focus on equilibrium systems, for which we show that coherent fluctuations add up to the fluctuations predicted by thermodynamic identities, valid for classical systems only. In the ground state, coherent fluctuations are the only ones to subsist, an in this case we study their relationship with entanglement entropy. We show in particular that an hypothesis of effective temperature, spatially modulated, captures the structure of entanglement in a many-body system, and we show how this temperature can be reconstructed from usual correlation functions. Our results also enable for a refined understanding of quantum phase transitions. We show in particular that the phase transition between a bosonic Mott insulator and a superfluid gives rise to a singularity of entanglement entropy induced by amplitude fluctuations of the superfluid order parameter. We finally identify a coherence length governing the scaling behaviour of coherent fluctuations inside the quantum critical region in the finite-temperature vicinity of a quantum critical point, and open novel perspectives for the metrological advantage offered by the exceptional coherence which develops close to quantum critical points, based on the example of the quantum Ising model.