Demonstration of a robust pseudogap in a three-dimensional correlated electronic system

We outline a partial-fractions decomposition method for determining the one-particle spectral function and single-particle density of states of a correlated electronic system on a finite lattice in the non self-consistent T-matrix approximation to arbitrary numerical accuracy, and demonstrate the application of these ideas to the attractive Hubbard model. We then demonstrate the effectiveness of a finite-size scaling ansatz which allows for the extraction of quantities of interest in the thermodynamic limit from this method. In this approximation, in one or two dimensions, for any finite lattice or in the thermodynamic limit, a pseudogap is present and its energy diverges as Tc is approached from above; this is an unphysical manifestation of using an approximation that predicts a spurious phase transition in one or two dimensions. However, in three dimensions one expects the transition predicted by this approximation to represent a true continuous phase transition, and in the thermodynamic limit any pseudogap predicted by this formulation will remain finite. We have applied our method to the attractive Hubbard model on a three-dimensional simple cubic lattice, and find that for intermediate coupling a prominent pseudogap is found in the single-particle density of states, and this gap persists over a large temperature range. In addition, we also show that for weak coupling a pseudogap is also present. The pseudogap energy at the transition temperature is almost a factor of three larger than the T=0 BCS gap for intermediate coupling, whereas for weak coupling the pseudogap and BCS gap energies are essentially equal.Comment: 28 pages, 9 figure

Multi-site mean-field theory for cold bosonic atoms in optical lattices

We present a detailed derivation of a multi-site mean-field theory (MSMFT) used to describe the Mott-insulator to superfluid transition of bosonic atoms in optical lattices. The approach is based on partitioning the lattice into small clusters which are decoupled by means of a mean field approximation. This approximation invokes local superfluid order parameters defined for each of the boundary sites of the cluster. The resulting MSMFT grand potential has a non-trivial topology as a function of the various order parameters. An understanding of this topology provides two different criteria for the determination of the Mott insulator superfluid phase boundaries. We apply this formalism to $d$-dimensional hypercubic lattices in one, two and three dimensions, and demonstrate the improvement in the estimation of the phase boundaries when MSMFT is utilized for increasingly larger clusters, with the best quantitative agreement found for $d=3$. The MSMFT is then used to examine a linear dimer chain in which the on-site energies within the dimer have an energy separation of $\Delta$. This system has a complicated phase diagram within the parameter space of the model, with many distinct Mott phases separated by superfluid regions.Comment: 30 pages, 23 figures, accepted for publication in Phys. Rev.

Thermal Analyzer for Planetary Soil (TAPS): an in Situ Instrument for Mineral and Volatile-element Measurements

Thermal Analyzer for Planetary Soil (TAPS) offers a specific implementation for the generic thermal analyzer/evolved-gas analyzer (TA/EGA) function included in the Mars Environmental Survey (MESUR) strawman payload; applications to asteroids and comets are also possible. The baseline TAPS is a single-sample differential scanning calorimeter (DSC), backed by a capacitive-polymer humidity sensor, with an integrated sampling mechanism. After placement on a planetary surface, TAPS acquires 10-50 mg of soil or sediment and heats the sample from ambient temperature to 1000-1300 K. During heating, DSC data are taken for the solid and evolved gases are swept past the water sensor. Through ground based data analysis, multicomponent DSC data are deconvolved and correlated with the water release profile to quantitatively determine the types and relative proportions of volatile-bearing minerals such as clays and other hydrates, carbonates, and nitrates. The rapid-response humidity sensors also achieve quantitative analysis of total water. After conclusion of soil-analysis operations, the humidity sensors become available for meteorology. The baseline design fits within a circular-cylindrical volume less than 1000 cm(sup 3), occupies 1.2 kg mass, and consumes about 2 Whr of power per analysis. Enhanced designs would acquire and analyze multiple samples and employ additional microchemical sensors for analysis of CO2, SO2, NO(x), and other gaseous species. Atmospheric pumps are also being considered as alternatives to pressurized purge gas

Optical conductivity of a metal-insulator transition for the Anderson-Hubbard model in 3 dimensions away from 1/2 filling

We have completed a numerical investigation of the Anderson-Hubbard model for three-dimensional simple cubic lattices using a real-space self-consistent Hartree-Fock decoupling approximation for the Hubbard interaction. In this formulation we treat the spatial disorder exactly, and therefore we account for effects arising from localization physics. We have examined the model for electronic densities well away 1/2 filling, thereby avoiding the physics of a Mott insulator. Several recent studies have made clear that the combined effects of electronic interactions and spatial disorder can give rise to a suppression of the electronic density of states, and a subsequent metal-insulator transition can occur. We augment such studies by calculating the ac conductivity for such systems. Our numerical results show that weak interactions enhance the density of states at the Fermi level and the low-frequency conductivity, there are no local magnetic moments, and the ac conductivity is Drude-like. However, with a large enough disorder strength and larger interactions the density of states at the Fermi level and the low-frequency conductivity are both suppressed, the conductivity becomes non-Drude-like, and these phenomena are accompanied by the presence of local magnetic moments. The low-frequency conductivity changes from a sigma-sigma_dc omega^{1/2} behaviour in the metallic phase, to a sigma omega^2 behaviour in the nonmetallic regime. Our numerical results show that the formation of magnetic moments is essential to the suppression of the density of states at the Fermi level, and therefore essential to the metal-insulator transition

Application of a multi-site mean-field theory to the disordered Bose-Hubbard model

We present a multi-site formulation of mean-field theory applied to the disordered Bose-Hubbard model. In this approach the lattice is partitioned into clusters, each isolated cluster being treated exactly, with inter-cluster hopping being treated approximately. The theory allows for the possibility of a different superfluid order parameter at every site in the lattice, such as what has been used in previously published site-decoupled mean-field theories, but a multi-site formulation also allows for the inclusion of spatial correlations allowing us, e.g., to calculate the correlation length (over the length scale of each cluster). We present our numerical results for a two-dimensional system. This theory is shown to produce a phase diagram in which the stability of the Mott insulator phase is larger than that predicted by site-decoupled single-site mean-field theory. Two different methods are given for the identification of the Bose glass-to-superfluid transition, one an approximation based on the behaviour of the condensate fraction, and one of which relies on obtaining the spatial variation of the order parameter correlation. The relation of our results to a recent proposal that both transitions are non self-averaging is discussed.Comment: Accepted for publication in Physical Review