Thermodynamics in the vicinity of a relativistic quantum critical point in 2+1 dimensions.

We study the thermodynamics of the relativistic quantum O(N) model in two space dimensions. In the vicinity of the zero-temperature quantum critical point (QCP), the pressure can be written in the scaling form P(T)=P(0)+N(T(3)/c(2))F(N)(Δ/T), where c is the velocity of the excitations at the QCP and |Δ| a characteristic zero-temperature energy scale. Using both a large-N approach to leading order and the nonperturbative renormalization group, we compute the universal scaling function F(N). For small values of N (N/~1) regimes, but fails to describe the nonmonotonic behavior of F(N) in the quantum critical regime. We discuss the renormalization-group flows in the various regimes near the QCP and make the connection with the quantum nonlinear sigma model in the renormalized classical regime. We compute the Berezinskii-Kosterlitz-Thouless transition temperature in the quantum O(2) model and find that in the vicinity of the QCP the universal ratio T(BKT)/ρ(s)(0) is very close to π/2, implying that the stiffness ρ(s)(T(BKT)(-)) at the transition is only slightly reduced with respect to the zero-temperature stiffness ρ(s)(0). Finally, we briefly discuss the experimental determination of the universal function F(2) from the pressure of a Bose gas in an optical lattice near the superfluid-Mott-insulator transition.

Confinement and superfluidity in one-dimensional degenerate fermionic cold atoms.

The physical properties of arbitrary half-integer spins F = N - (1/2) fermionic cold atoms trapped in a one-dimensional optical lattice are investigated by means of a low-energy approach. Two different superfluid phases are found for F > or = (3/2) depending on whether a discrete symmetry is spontaneously broken or not: an unconfined BCS pairing phase and a confined molecular-superfluid instability made of 2N fermions. We propose an experimental distinction between these phases for a gas trapped in an annular geometry. The confined-unconfined transition is shown to belong to the Z(N) generalized Ising universality class. We discuss the possible Mott phases at (1/2) filling.

Spontaneous plaquette formation in the SU(4) spin-orbital ladder.

The low-energy properties of the SU(4) spin-orbital model on a two-leg ladder are studied by a variety of analytical and numerical techniques. As in the case of SU(2) models, there is a singlet-multiplet gap in the spectrum, but the ground state is twofold degenerate. An interpretation in terms of SU(4)-singlet plaquettes is proposed. The implications for general two-dimensional lattices are outlined.