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Recent advances in cooling techniques make now possible the experimental study of quantum phase transitions, which are transitions near absolute zero temperature accessed by varying a control parameter. A paradigmatic example is the superfluid-Mott transition of interacting bosons on a periodic lattice. From the relativistic Ginzburg-Landau action of this superfluid-Mott transition we derive the elementary excitations of the bosonic system, which contain in the superfluid phase a gapped Higgs mode and a gappless Goldstone mode. We show that this energy spectrum is in good agreement with the available experimental data and we use it to extract, with the help of dimensional regularization, meaningful analytical formulas for the beyond-mean-field equation of state in two and three spatial dimensions. We find that, while the mean-field equation of state always gives a second-order quantum phase transition, the inclusion of Gaussian quantum fluctuations can induce a first-order quantum phase transition. This prediction is a strong benchmark for next future experiments on quantum phase transitions.
We study the thermodynamics near the generic (density-driven) superfluid--Mott-insulator transition in the three-dimensional Bose-Hubbard model using the nonperturbative renormalization-group approach. At low energy the physics is controlled by the G
We study near-equilibrium thermodynamics of bosonic atoms in a two-dimensional optical lattice by ramping up the lattice depth to convert a superfluid into an inhomogeneous mixture of superfluid and Mott insulator. Detailed study of in situ density p
The coexistence of superfluid and Mott insulator, due to the quadratic confinement potential in current optical lattice experiments, makes the accurate detection of the superfluid-Mott transition difficult. Studying alternative trapping potentials wh
We report on a novel structural Superfluid-Mott Insulator (SF-MI) quantum phase transition for an interacting one-dimensional Bose gas within permeable multi-rod lattices, where the rod lengths are varied from zero to the lattice period length. We us
We present a universal theory for the critical behavior of an impurity at the two-dimensional superfluid-Mott insulator transition. Our analysis is motivated by a numerical study of the Bose-Hubbard model with an impurity site by Huang et al. (Phys.