Consequences of the Pauli exclusion principle for the Bose-Einstein condensation of atoms and excitons

The bosonic atoms used in present day experiments on Bose-Einstein condensation are made up of fermionic electrons and nucleons. In this Letter we demonstrate how the Pauli exclusion principle for these constituents puts an upper limit on the Bose-Einstein-condensed fraction. Detailed numerical results are presented for hydrogen atoms in a cubic volume and for excitons in semiconductors and semiconductor bilayer systems. The resulting condensate depletion scales differently from what one expects for bosons with a repulsive hard-core interaction. At high densities, Pauli exclusion results in significantly more condensate depletion. These results also shed a new light on the low condensed fraction in liquid helium II.Comment: 4 pages, 2 figures, revised version, now includes a direct comparison with hard-sphere QMC results, submitted to Phys. Rev. Let

From the Cooper problem to canted supersolids in Bose-Fermi mixtures

We calculate the phase diagram of the Bose-Fermi Hubbard model on the 3d cubic lattice at fermionic half filling and bosonic unit filling by means of single-site dynamical mean-field theory. For fast bosons, this is equivalent to the Cooper problem in which the bosons can induce s-wave pairing between the fermions. We also find miscible superfluid and canted supersolid phases depending on the interspecies coupling strength. In contrast, slow bosons favor fermionic charge density wave structures for attractive fermionic interactions. These competing instabilities lead to a rich phase diagram within reach of cold gas experiments.Comment: 5 pages, 4 figures; replaced with published versio

Stochastic Mean-Field Theory for the Disordered Bose-Hubbard Model

We investigate the effect of diagonal disorder on bosons in an optical lattice described by an Anderson-Hubbard model at zero temperature. It is known that within Gutzwiller mean-field theory spatially resolved calculations suffer particularly from finite system sizes in the disordered case, while arithmetic averaging of the order parameter cannot describe the Bose glass phase for finite hopping $J>0$. Here we present and apply a new \emph{stochastic} mean-field theory which captures localization due to disorder, includes non-trivial dimensional effects beyond the mean-field scaling level and is applicable in the thermodynamic limit. In contrast to fermionic systems, we find the existence of a critical hopping strength, above which the system remains superfluid for arbitrarily strong disorder.Comment: 6 pages, 6 figure

Regularization of Diagrammatic Series with Zero Convergence Radius

The divergence of perturbative expansions for the vast majority of macroscopic systems, which follows from Dyson's collapse argument, prevents Feynman's diagrammatic technique from being directly used for controllable studies of strongly interacting systems. We show how the problem of divergence can be solved by replacing the original model with a convergent sequence of successive approximations which have a convergent perturbative series. As a prototypical model, we consider the zero-dimensional $\vert \psi \vert^4$ theory.Comment: 4 pages, 3 figure

Facebook Social Use and Anxiety: A Replication Attempt

The relationship between social media use and mental health remains under scrutiny by researchers, policy makers, and the general public. Recently, researchers have addressed whether Facebook use is beneficial to people with high social anxiety. The findings from such studies are mixed, partly due to differences in how variables are operationalised. A study by McCord et al (McCord, B., Rodebaugh, T. L., & Levinson, C. A., 2014. Facebook: Social uses and anxiety.  Computers in Human Behavior, 34, 23-27) suggested that the inclusion of a new variable, Facebook-centric social anxiety, helps explain the complex relationship between general social anxiety and frequency of usage of socially-interactive Facebook features. We undertook two studies (N=202 and N=542; majority British and non-student participants) with the aim of replicating McCord et al (2014), using the original measures (general social anxiety, Facebook-centric social anxiety, and frequency of usage of socially-interactive Facebook features). Replicating the original study, we found a significant positive association between general social anxiety and Facebook-centric social anxiety. However, unlike the original study, we did not find evidence that general social anxiety and Facebook-centric social anxiety interacted to predict frequency of usage of socially-interactive Facebook features. We discuss the implications for future research on social Facebook use

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

Dynamical mean field solution of the Bose-Hubbard model

We present the effective action and self-consistency equations for the bosonic dynamical mean field (B-DMFT) approximation to the bosonic Hubbard model and show that it provides remarkably accurate phase diagrams and correlation functions. To solve the bosonic dynamical mean field equations we use a continuous-time Monte Carlo method for bosonic impurity models based on a diagrammatic expansion in the hybridization and condensate coupling. This method is readily generalized to bosonic mixtures, spinful bosons, and Bose-Fermi mixtures.Comment: 10 pages, 3 figures. includes supplementary materia

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

Quantum Monte Carlo simulation in the canonical ensemble at finite temperature

A quantum Monte Carlo method with non-local update scheme is presented. The method is based on a path-integral decomposition and a worm operator which is local in imaginary time. It generates states with a fixed number of particles and respects other exact symmetries. Observables like the equal-time Green's function can be evaluated in an efficient way. To demonstrate the versatility of the method, results for the one-dimensional Bose-Hubbard model and a nuclear pairing model are presented. Within the context of the Bose-Hubbard model the efficiency of the algorithm is discussed.Comment: 11 pages, 8 figure

Finite-temperature effects on the superfluid Bose-Einstein condensation of confined ultracold atoms in three-dimensional optical lattices

We discuss the finite-temperature phase diagram in the three-dimensional Bose-Hubbard (BH) model in the strong correlation regime, relevant for Bose-Einstein condensates in optical lattices, by employing a quantum rotor approach. In systems with strong on site repulsive interactions, the rotor U(1) phase variable dual to the local boson density emerges as an important collective field. After establishing the connection between the rotor construction and the the on--site interaction in the BH model the robust effective action formalism is developed which allows us to study the superfluid phase transition in various temperature--interaction regimes