Non Perturbative Renormalization Group, momentum dependence of nn-point functions and the transition temperature of the weakly interacting Bose gas

We propose a new approximation scheme to solve the Non Perturbative Renormalization Group equations and obtain the full momentum dependence of $n$-point functions. This scheme involves an iteration procedure built on an extension of the Local Potential Approximation commonly used within the Non Perturbative Renormalization Group. Perturbative and scaling regimes are accurately reproduced. The method is applied to the calculation of the shift $\Delta T_c$ in the transition temperature of the weakly repulsive Bose gas, a quantity which is very sensitive to all momenta intermediate between these two regions. The leading order result is in agreement with lattice calculations, albeit with a theoretical uncertainty of about 25%. The next-to-leading order differs by about 10% from the best accepted result

Low energy monopole Modes of a Trapped atomic Fermi Gas

We consider the low energy collective monopole modes of a trapped weakly interacting atomic Fermi gas in the collisionless regime. The spectrum is calculated for varying coupling strength and chemical potential. Using an effective Hamiltonian, we derive analytical results that agree well with numerical calculations in various regimes. The onset of superfluidity is shown to lead to effects such as the vanishing of the energy required to create a Cooper molecule at a critical coupling strength and to the emergence of pair vibration excitations. Our analysis suggests ways to experimentally detect the presence of the superfluid phase in trapped atomic Fermi gases.Comment: 5 pages & 1 figure. Accepted for Phys. Rev. Let

From Trapped Atoms to Liberated Quarks

We discuss some aspects of cold atomic gases in the unitarity limit that are of interest in connection with the physics of dense hadronic matter. We consider, in particular, the equation of state at zero temperature, the magnitude of the pairing gap, and the phase diagram at non-zero polarization.Comment: 13 pages, 5 figures; to appear in the proceedings of the International Symposium on Heavy Ion Physics 2006, Frankfurt, Germany; International Journal of Modern Physics E, in pres

Non perturbative renormalization group and momentum dependence of n-point functions (II)

In a companion paper (hep-th/0512317), we have presented an approximation scheme to solve the Non Perturbative Renormalization Group equations that allows the calculation of the $n$-point functions for arbitrary values of the external momenta. The method was applied in its leading order to the calculation of the self-energy of the O($N$) model in the critical regime. The purpose of the present paper is to extend this study to the next-to-leading order of the approximation scheme. This involves the calculation of the 4-point function at leading order, where new features arise, related to the occurrence of exceptional configurations of momenta in the flow equations. These require a special treatment, inviting us to improve the straightforward iteration scheme that we originally proposed. The final result for the self-energy at next-to-leading order exhibits a remarkable improvement as compared to the leading order calculation. This is demonstrated by the calculation of the shift $\Delta T_c$, caused by weak interactions, in the temperature of Bose-Einstein condensation. This quantity depends on the self-energy at all momentum scales and can be used as a benchmark of the approximation. The improved next-to-leading order calculation of the self-energy presented in this paper leads to excellent agreement with lattice data and is within 4% of the exact large $N$ result.Comment: 35 pages, 11 figure

Energy weighted sum rules for mesons in hot and dense matter

We study energy weighted sum rules of the pion and kaon propagator in nuclear matter at finite temperature. The sum rules are obtained from matching the Dyson form of the meson propagator with its spectral Lehmann representation at low and high energies. We calculate the sum rules for specific models of the kaon and pion self-energy. The in-medium spectral densities of the K and anti-K mesons are obtained from a chiral unitary approach in coupled channels which incorporates the S- and P-waves of the kaon-nucleon interaction. The pion self-energy is determined from the P-wave coupling to particle-hole and Delta-hole excitations, modified by short range correlations. The sum rules for the lower energy weights are fulfilled satisfactorily and reflect the contributions from the different quasi-particle and collective modes of the meson spectral function. We discuss the sensitivity of the sum rules to the distribution of spectral strength and their usefulness as quality tests of model calculations.Comment: 19 pages, 6 figures; one figure added, enhanced discussion, version to appear in PR

LeMoMaF: Lensed Mock Map Facility

We present the Lensed Mock Map Facility (LeMoMaF), a tool designed to perform mock weak lensing measurements on numerically simulated chunks of the universe. Coupling N-body simulations to a semi-analytical model of galaxy formation, LeMoMaF can create realistic lensed images and mock catalogues of galaxies, at wavelengths ranging from the UV to the submm. To demonstrate the power of such a tool we compute predictions of the source-lens clustering effect on the convergence statistics, and quantify the impact of weak lensing on galaxy counts in two different filters. We find that the source-lens clustering effect skews the probability density function of the convergence towards low values, with an intensity which strongly depends on the redshift distribution of galaxies. On the other hand, the degree of enhancement or depletion in galaxy counts due to weak lensing is independent of the source-lens clustering effect. We discuss the impact on the two-points shear statistics to be measured by future missions like SNAP and LSST. The source-lens clustering effect would bias the estimation of sigma_8 from two point statistics by 2% -5%. We conclude that accurate photometric redshifts for individual galaxies are necessary in order to quantify and isolate the source-lens clustering effect.Comment: 14 pages, 11 figures, submitted to MNRA

On interacting fermions and bosons with definite total momentum

Any {\it exact} eigenstate with a definite momentum of a many-body Hamiltonian can be written as an integral over a {\it symmetry-broken} function $\Phi$. For two particles, we solve the problem {\it exactly} for all energy levels and any inter-particle interaction. Especially for the ground-state, $\Phi$ is given by the simple Hartree-Fock/Hartree ansatz for fermions/bosons. Implications for several and many particles as well as a numerical example are provided

Unconventional Spin Density Waves in Dipolar Fermi Gases

The conventional spin density wave (SDW) phase (Overhauser, 1962), as found in antiferromagnetic metal for example (Fawcett 1988), can be described as a condensate of particle-hole pairs with zero angular momentum, $\ell=0$, analogous to a condensate of particle-particle pairs in conventional superconductors. While many unconventional superconductors with Cooper pairs of finite $\ell$ have been discovered, their counterparts, density waves with non-zero angular momenta, have only been hypothesized in two-dimensional electron systems (Nayak, 2000). Using an unbiased functional renormalization group analysis, we here show that spin-triplet particle-hole condensates with $\ell=1$ emerge generically in dipolar Fermi gases of atoms (Lu, Burdick, and Lev, 2012) or molecules (Ospelkaus et al., 2008; Wu et al.) on optical lattice. The order parameter of these exotic SDWs is a vector quantity in spin space, and, moreover, is defined on lattice bonds rather than on lattice sites. We determine the rich quantum phase diagram of dipolar fermions at half-filling as a function of the dipolar orientation, and discuss how these SDWs arise amidst competition with superfluid and charge density wave phases.Comment: 5 pages, 3 figure

Ferromagnetically coupled dimers on the distorted Shastry-Sutherland lattice: Application to (CuCl)LaNb2O7

A recent study [Tassel {\it et al.}, Phys. Rev. Lett. {\bf 105}, 167205 (2010)] has proposed a remarkable spin model for (CuCl)LaNb2O7, in which dimers are ferromagnetically coupled to each other on the distorted Shastry-Sutherland lattice. In this model, the intra-dimer exchange coupling J>0 is antiferromagnetic, while the inter-dimer exchange couplings are ferromagnetic and take different values, J_x,J_y<0, in the two bond directions. Anticipating that the highly frustrated character of this model may lead to a wide range of behaviors in (CuCl)LaNb2O7 and related compounds, we theoretically investigate the ground state phase diagram of this model in detail using the following three approaches: a strong-coupling expansion for small J_x and J_y, exact diagonalization for finite clusters, and a Schwinger boson mean field theory. When |J_x|, |J_y| <~ J, the system stays in a dimer singlet phase with a finite spin gap. This state is adiabatically connected to the decoupled-dimer limit J_x=J_y=0. We show that the magnetization process of this phase depends crucially on the spatial anisotropy of the inter-dimer couplings. The magnetization shows a jump or a smooth increase for weak and strong anisotropy, respectively, after the spin gap closes at a certain magnetic field. When |J_x| or |J_y| >~ J, quantum phase transitions to various magnetically ordered phases (ferromagnetic, collinear stripe, and spiral) occur. The Schwinger boson analysis demonstrates that quantum fluctuations split the classical degeneracy of different spiral ground states. Implications for (CuCl)LaNb2O7 and related compounds are discussed in light of our theoretical results and existing experimental data.Comment: 21 pages, 20 figure