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We present a strong-coupling expansion of the Bose-Hubbard model which describes both the superfluid and the Mott phases of ultracold bosonic atoms in an optical lattice. By performing two successive HubbardStratonovich transformations of the intersite hopping term, we derive an effective action which provides a suitable starting point to study the strong-coupling limit of the Bose-Hubbard model. This action can be analyzed by taking into account Gaussian fluctuations about the mean-field approximation as in the Bogoliubov theory of the weakly interacting Bose gas. In the Mott phase, we reproduce results of previous mean-field theories and also calculate the momentum distribution function. In the superfluid phase, we find a gapless spectrum and compare our results with the Bogoliubov theory.

We determine the phase diagram of a quasi-one-dimensional conductor (weakly coupled chains system with an open Fermi surface) in a magnetic field. The usual Ginzburg-Landau regime is followed, when the field is increased, by a cascade of superconducting phases separated by first order transitions, which ends with a strong reentrance of the superconducting phase. These new phases show a novel kind of symmetry of laminar type. The Zeeman splitting does not completely suppress the reentrance in very strong field, the ground state being in this case a Larkin-Ovchinnikov-Fulde-Ferrell state.

We propose an implementation of the nonperturbative renormalization group (NPRG) which applies to lattice models. Contrary to the usual NPRG approach where the initial condition of the RG flow is the mean-field solution, the lattice NPRG uses the (local) limit of decoupled sites as the (initial) reference system. In the long-distance limit, it is equivalent to the usual NPRG formulation and therefore yields identical results for the critical properties. We discuss both a lattice field theory defined on a d-dimensional hypercubic lattice and classical spin models. The simplest approximation, the local potential approximation, is sufficient to obtain the critical temperature and the magnetization of the three-dimensional Ising, XY, and Heisenberg models to an accuracy on the order of 1%. We show how the local potential approximation can be improved to include a nonzero anomalous dimension η and discuss the Berezinskii-Kosterlitz-Thouless transition of the two-dimensional XY model on a square lattice.

Using a renormalization group approach, we determine the phase diagram of an extended quasi-one-dimensional electron gas model that includes interchain hopping, nesting deviations, and both intrachain and interchain repulsive interactions. We find a close proximity of spin-density- and charge-density-wave phases and singlet d-wave and triplet f-wave superconducting phases. There is a striking correspondence between our results and recent puzzling experimental findings in the Bechgaard salts, including the coexistence of spin-density-wave and charge-density-wave phases and the possibility of a triplet pairing in the superconducting phase.

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We determine the phase diagram of a quasi-one-dimensional superconductor (weakly coupled chains system with an open Fermi surface) in a magnetic field. A field H (O, H, O) along the y direction (perpendicular the direction 2: of highest conductivity) tends to confine the electronic motion in the z direction. At low temperature, this efFect cannot be neglected and the Ginzburg-Landau theory breaks down. We find that the usual Ginzburg-Landau regime is followed, when the field is increased, by a cascade of superconducting phases separated by first-order transitions, which ends with a strong reentrance of the superconducting phase where the chains interact by Josephson coupling. This high-field superconductivity can survive even in the presence of Pauli pair breaking because the quasi-one-dimensional Fermi surface allows one to construct a Larkin-Ovchinnikov-Fulde-Ferrell state that can exist far above the Pauli-limited field. Moreover, elastic scattering does not destroy the superconducting phases in clean materials with sufBciently large anisotropy. We show that the superconducting state evolves from an Abrikosov vortex lattice in weak field towards a Josephson vortex lattice in the reentrant phase. Between these two limits, the order parameter and the current distribution show laminar-type symmetry. The relevance of our results is discussed for quasi-one-dimensional organic superconductors and quasi-two-dimensional superconductors.

We use a non-perturbative renormalization group technique to study interacting bosons at zero temperature. Our approach reveals the instability of the Bogoliubov fixed point when d 3 and yields the exact infrared behavior in all dimensions d > 1 within a rather simple theoretical framework. It also enables to compute the low-energy properties in terms of the parameters of a microscopic model. In one dimension and for not too strong interactions, it yields a good picture of the Luttinger-liquid behavior of the superfluid phase.