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Résumé |
In this talk we will consider interacting bosons on a lattice (in dimensions greater than one), described by the Bose-Hubbard model. We discuss superfluidity and quantum criticality near the Mott transition using a non-perturbative renormalization-group approach. This approach reproduces the phase diagram of the model (in very good quantitative agreement with the numerically exact Quantum Monte Carlo result) and captures the two universality classes of the Mott transition. Near the density-driven Mott transition, the pressure P(mu,T) is fully determined by a universal scaling function, characteristic of the dilute Bose gas universality class, and two non-universal parameters m^* and a^* which depend on the ratio t/U between hopping amplitude and onsite repulsion. m^* is the mass of the elementary excitations at the T=0 quantum critical point between the superfluid and the Mott-insulating phases, while a^* is a "scattering length" related to the effective interaction at low energy. Finally, we compare our theoretical results with recent experiments on the thermodynamics of a two-dimensional Bose gas, with or without an optical lattice. |
