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Corrélations, intrication et dynamique des systèmes quantiques à N Corps : une étude variationnelle

Abstract : This thesis presents a study of quantum many-body systems at zero temperature, where the behavior of the system is purely driven by the quantum effects. I will introduce a variationnal approach developped with Tommaso Roscilde, my PhD supervisor, and Fabio Mezzacapo, my co-supervisor, in order to study these systems.This approach is based on a parametrisation of the quantum state (named Ansatz) on which we apply a variational optimisation, allowing us reproduce the system's evolution under Schrödinger's equation with a limited number of variables.By considering an imaginary-time evolution, it is possible to reconstruct the system's ground state. I focused on S=1/2 XX spin chain, where the long-range quantum correlations complicate a variational study; and I have specifically targeted our Ansatz in order to reproduce the correlations and the entanglement of the ground state. Moreover I considered the antiferromagnetic S=1/2 J1-J2 spin chain, where the non-trivial sign structure of the coefficients of the quantum state introduces an important challenge for the quantum Monte Carlo approach; and where the magnetic frustration induces a quantum phase transition (from a state with long range correlations to a non-magnetic state in the form of a valence-bond crystal).Finally I focused on the time evolution of a quantum many-body system starting from a non-stationary state. I studied the ability of our approach to reproduce the linear increase of the entanglement during time, which is a fondamental obstacle for other approaches such as the density-matrix renormalization group.
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Submitted on : Monday, November 4, 2019 - 3:44:30 PM
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Jérôme Thibaut. Corrélations, intrication et dynamique des systèmes quantiques à N Corps : une étude variationnelle. Electrons fortement corrélés [cond-mat.str-el]. Université de Lyon, 2019. Français. ⟨NNT : 2019LYSEN021⟩. ⟨tel-02345613⟩

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