Bosons Confined in Optical Lattices: the Numerical Renormalization Group revisited

A Bose-Hubbard model, describing bosons in a harmonic trap with a superimposed optical lattice, is studied using a fast and accurate variational technique (MF+NRG): the Gutzwiller mean-field (MF) ansatz is combined with a Numerical Renormalization Group (NRG) procedure in order to improve on both. Results are presented for one, two and three dimensions, with particular attention to the experimentally accessible momentum distribution and possible satellite peaks in this distribution. In one dimension, a comparison is made with exact results obtained using Stochastich Series Expansion.Comment: 10 pages, 15 figure

Integrable two-channel p_x+ip_y-wave superfluid model

We present a new two-channel integrable model describing a system of spinless fermions interacting through a p-wave Feshbach resonance. Unlike the BCS-BEC crossover of the s-wave case, the p-wave model has a third order quantum phase transition. The critical point coincides with the deconfinement of a single molecule within a BEC of bound dipolar molecules. The exact many-body wavefunction provides a unique perspective of the quantum critical region suggesting that the size of the condensate wavefunction, that diverges logarithmically with the chemical potential, could be used as an experimental indicator of the phase transition.Comment: 4 pages, 4 figure

Ultracold atoms in one-dimensional optical lattices approaching the Tonks-Girardeau regime

Recent experiments on ultracold atomic alkali gases in a one-dimensional optical lattice have demonstrated the transition from a gas of soft-core bosons to a Tonks-Girardeau gas in the hard-core limit, where one-dimensional bosons behave like fermions in many respects. We have studied the underlying many-body physics through numerical simulations which accommodate both the soft-core and hard-core limits in one single framework. We find that the Tonks-Girardeau gas is reached only at the strongest optical lattice potentials. Results for slightly higher densities, where the gas develops a Mott-like phase already at weaker optical lattice potentials, show that these Mott-like short range correlations do not enhance the convergence to the hard-core limit.Comment: 4 pages, 3 figures, replaced with published versio

Integrable models for asymmetric Fermi superfluids: Emergence of a new exotic pairing phase

We introduce an exactly-solvable model to study the competition between the Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) and breached-pair superfluid in strongly interacting ultracold asymmetric Fermi gases. One can thus investigate homogeneous and inhomogeneous states on an equal footing and establish the quantum phase diagram. For certain values of the filling and the interaction strength, the model exhibits a new stable exotic pairing phase which combines an inhomogeneous state with an interior gap to pair-excitations. It is proven that this phase is the exact ground state in the strong coupling limit, while numerical examples demonstrate that also at finite interaction strength it can have lower energy than the breached-pair or LOFF states.Comment: Revised version accepted for publicatio

Maximum occupation number for composite boson states

One of the major differences between fermions and bosons is that fermionic states have a maximum occupation number of one, whereas the occupation number for bosonic states is in principle unlimited. For bosons that are made up of fermions, one could ask the question to what extent the Pauli principle for the constituent fermions would limit the boson occupation number. Intuitively one can expect the maximum occupation number to be proportional to the available volume for the bosons divided by the volume occupied by the fermions inside one boson, though a rigorous derivation of this result has not been given before. In this letter we show how the maximum occupation number can be calculated from the ground-state energy of a fermionic generalized pairing problem. A very accurate analytical estimate of this eigenvalue is derived. From that a general expression is obtained for the maximum occupation number of a composite boson state, based solely on the intrinsic fermionic structure of the bosons. The consequences for Bose-Einstein condensates of excitons in semiconductors and ultra cold trapped atoms are discussed.Comment: 4 pages, Revte

A quantum Monte-Carlo method for fermions, free of discretization errors

In this work we present a novel quantum Monte-Carlo method for fermions, based on an exact decomposition of the Boltzmann operator $exp(-\beta H)$. It can be seen as a synthesis of several related methods. It has the advantage that it is free of discretization errors, and applicable to general interactions, both for ground-state and finite-temperature calculations. The decomposition is based on low-rank matrices, which allows faster calculations. As an illustration, the method is applied to an analytically solvable model (pairing in a degenerate shell) and to the Hubbard model.Comment: 5 pages, 4 figures, submitted to Phys. Rev. Let

Solving the Richardson equations for Fermions

Forty years ago Richardson showed that the eigenstates of the pairing Hamiltonian with constant interaction strength can be calculated by solving a set of non-linear coupled equations. However, in the case of Fermions these equations lead to singularities which made them very hard to solve. This letter explains how these singularities can be avoided through a change of variables making the Fermionic pairing problem numerically solvable for arbitrary single particle energies and degeneracies.Comment: 5 pages, 4 figures, submitted to Phys.Rev.

Cross-sections for neutral-current neutrino-nucleus interactions: applications for 12^{12}C and 16^{16}O

We calculate cross sections for neutral current quasi-elastic neutrino-nucleus scattering within a continuum RPA model, based on a Green's function approach. As residual interaction a Skyrme force is used. The unperturbed single particle wave functions are generated using either a Woods-Saxon potential or a Hartree-Fock calculation. These calculations have interesting applications. Neutrinos play an important role in supernova nucleosynthesis. To obtain more information about these processes, cross sections are folded with a Fermi-Dirac distribution with temperatures of approximately 10$^9$ K

Optimal Monte Carlo Updating

Based on Peskun's theorem it is shown that optimal transition matrices in Markov chain Monte Carlo should have zero diagonal elements except for the diagonal element corresponding to the largest weight. We will compare the statistical efficiency of this sampler to existing algorithms, such as heat-bath updating and the Metropolis algorithm. We provide numerical results for the Potts model as an application in classical physics. As an application in quantum physics we consider the spin 3/2 XY model and the Bose-Hubbard model which have been simulated by the directed loop algorithm in the stochastic series expansion framework.Comment: 6 pages, 5 figures, replaced with published versio

Exactly solvable pairing Hamiltonian for heavy nuclei

We present a new exactly solvable Hamiltonian with a separable pairing interaction and non-degenerate single-particle energies. It is derived from the hyperbolic family of Richardson-Gaudin models and possesses two free parameters, one related to an interaction cutoff and the other to the pairing strength. These two parameters can be adjusted to give an excellent reproduction of Gogny self-consistent mean-field calculations in the canonical basis.Comment: 4 pages, 3 figure