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Criticalité quantique et universalité d'un gaz de Bose au voisinage de la transition de Mott

Abstract : We study the quantum phase transition from the superfluid to the Mott insu- lator in the framework of the Bose-Hubbard model, which describes lattice bosons with on-site interactions. We implement a lattice formulation of the non-perturbative renormalization group, whose initial condition is the local limit (limit of decoupled sites). The results are in quantitative agreement for universal quantities (existence of two universality classes, critical exponents consistent with those expected) and non-universal ones (e.g. phase diagrams in accordance with the best numerical ap- proaches). The density-driven Mott transition belongs to the universality class of the vacuum-superfluid transition of a dilute Bose gas. By characterizing the elementary excitations at the quantum critical point as bosonic quasiparticles, with effective mass m∗ and quasiparticle weight ZQP, whose interactions are given by an effec- tive "scattering length" a∗, we describe the universal thermodynamics near the Mott transition using the scaling functions of the dilute Bose gas. We also calculate the nontrivial scaling functions in two dimensions at finite temperature and compare them to recent experiments, demonstrating the universality of dilute Bose gases.
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Contributor : Adam Rançon Connect in order to contact the contributor
Submitted on : Friday, December 7, 2012 - 3:38:00 PM
Last modification on : Sunday, June 26, 2022 - 10:02:01 AM
Long-term archiving on: : Saturday, December 17, 2016 - 9:12:29 PM

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  • HAL Id : tel-00761694, version 1

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Adam Rançon. Criticalité quantique et universalité d'un gaz de Bose au voisinage de la transition de Mott. Physique [physics]. Université Pierre et Marie Curie - Paris VI, 2012. Français. ⟨NNT : ⟩. ⟨tel-00761694⟩

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