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Corrélations dans les systèmes quantiques inhomogènes à une dimension

Abstract : One-dimensional quantum systems have long been seen as simple toy-models but are nowadays often realized in ultracold atoms experiments. In those experiments the confining potential creates a spatial inhomogeneity. This breaks the translation invariance which plays a key role in exact analytical solutions as the Bethe Ansatz. In this thesis, we propose an effective theory generalizing the Luttinger liquid approach for inhomogeneous systems. In this setup, the effective action lives in curved space. However, making the hypothesis of separation of scales allow to compute the action's parameters by using Bethe Ansatz. The problem can then be solved in flat space by using tools from conformal theory. This leads us to solving the inhomogeneous gaussian free field that gives access to all correlation functions of the model under investigation. Here we focus on the Lieb-Liniger model. Our results are tested against DMRG simulations.
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Submitted on : Wednesday, December 4, 2019 - 3:07:08 PM
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  • HAL Id : tel-02393790, version 1



Yannis Brun. Corrélations dans les systèmes quantiques inhomogènes à une dimension. Physique Quantique [quant-ph]. Université de Lorraine, 2019. Français. ⟨NNT : 2019LORR0094⟩. ⟨tel-02393790⟩



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