The Hubbard model with smooth boundary conditions

We apply recently developed smooth boundary conditions to the quantum Monte Carlo simulation of the two-dimensional Hubbard model. At half-filling, where there is no sign problem, we show that the thermodynamic limit is reached more rapidly with smooth rather than with periodic or open boundary conditions. Away from half-filling, where ordinarily the simulation cannot be carried out at low temperatures due to the existence of the sign problem, we show that smooth boundary conditions allow us to reach significantly lower temperatures. We examine pairing correlation functions away from half-filling in order to determine the possible existence of a superconducting state. On a $10\times 10$ lattice for $U=4$, at a filling of $\langle n \rangle = 0.87$ and an inverse temperature of $\beta=10$, we did find enhancement of the $d$-wave correlations with respect to the non-interacting case, a possible sign of $d$-wave superconductivity.Comment: 16 pages RevTeX, 9 postscript figures included (Figure 1 will be faxed on request

Oblique triangular antiferromagnetic phase in CsCu1−x_{1-x}Cox_xCl3_3

The spin-1/2 stacked triangular antiferromagnet CsCu$_{1-x}$Co$_x$Cl$_3$ with $0.015<x<0.032$ undergoes two phase transitions at zero field. The low-temperature phase is produced by the small amount of Co$^{2+}$ doping. In order to investigate the magnetic structures of the two ordered phases, the neutron elastic scattering experiments have been carried out for the sample with $x\approx 0.03$. It is found that the intermediate phase is identical to the ordered phase of CsCuCl$_3$, and that the low-temperature phase is an oblique triangular antiferromagnetic phase in which the spins form a triangular structure in a plane tilted from the basal plane. The tilting angle which is 42$^{\circ}$ at $T=1.6$ K decreases with increasing temperature, and becomes zero at $T_{\rm N2} =7.2$ K. An off-diagonal exchange term is proposed as the origin of the oblique phase.Comment: 6 pages, 7 figure

Detection of pairing correlation in the two-dimensional Hubbard model

Quantum Monte Carlo method is used to re-examine superconductivity in the single-band Hubbard model in two dimensions. Instead of the conventional pairing, we consider a `correlated pairing', \langle \tilde{c}_{i\uparrow} \tilde{c}_{i'\downarrow} %\tilde{c}_{j'\downarrow}^\dagger \tilde{c}_{j \uparrow}^\dagger \rangle with $\tilde{c}_{i\sigma} \equiv c_{i\sigma}(1-n_{i-\sigma})$, which is inferred from the $t$-$J$ model, the strong-coupling limit of the Hubbard model. The pairing in the $d$-wave channel is found to possess both a divergence like $1/T$ in the pairing susceptibility and a growth of the ground-state pairing correlation with sample size, indicating an off-diagonal long-range order near (but not exactly at) half-filling.Comment: 3 pages, revtex, 6 figures available on request from [email protected]

An Improved Upper Bound for the Ground State Energy of Fermion Lattice Models

We present an improved upper bound for the ground state energy of lattice fermion models with sign problem. The bound can be computed by numerical simulation of a recently proposed family of deformed Hamiltonians with no sign problem. For one dimensional models, we expect the bound to be particularly effective and practical extrapolation procedures are discussed. In particular, in a model of spinless interacting fermions and in the Hubbard model at various filling and Coulomb repulsion we show how such techniques can estimate ground state energies and correlation function with great accuracy.Comment: 5 pages, 5 figures; to appear in Physical Review

Effect of nearest neighbor repulsion on the low frequency phase diagram of a quarter-filled Hubbard-Holstein chain

We have studied the influence of nearest-neighbor (NN) repulsion on the low frequency phase diagram of a quarter-filled Hubbard-Holstein chain. The NN repulsion term induces the apparition of two new long range ordered phases (one $4k_F$ CDW for positive $U_{eff} = U-2g^2/\omega$ and one $2k_F$ CDW for negative $U_{eff}$) that did not exist in the V=0 phase diagram. These results are put into perspective with the newly observed charge ordered phases in organic conductors and an interpretation of their origin in terms of electron-molecular vibration coupling is suggested.Comment: 10 pages, 10 figure

Thermodynamic properties and thermal correlation lengths of a Hubbard model with bond-charge interaction

We investigate the thermodynamics of a one-dimensional Hubbard model with bond-charge interaction X using the transfer matrix renormalization group method (TMRG). Numerical results for various quantities like spin and charge susceptibilities, particle densities, specific heat and thermal correlation lengths are presented and discussed. We compare our data also to results for the exactly solvable case X/t=1 as well as to bosonisation results for weak coupling X/t << 1, which shows excellent agreement. We confirm the existence of a Tomonaga-Luttinger and a Luther-Emery liquid phase, in agreement with previous studies at zero temperature. Thermal singlet-pair correlation lengths are shown to dominate density and spin correlations for finite temperatures in certain parameter regimes.Comment: 13 pages, revte

Validating criteria for identifying core concepts using many-facet rasch measurement

Introduction: Core concepts are foundational, discipline-based ideas considered necessary for students to learn, remember, understand, and apply. To evaluate the extent to which a concept is “core,” experts often rate concepts using various criteria, such as importance, complexity, and timeliness. However, there is a lack of validity evidence for core concepts criteria. Methods: Using a three-facet Many-Facet Rasch Measurement (MFRM) model, we analyzed 7,558 ratings provided by 21 experts/raters for 74 pharmacology core concepts using five criteria measured on a five-point scale. Results: All of the criteria had Infit or Outfit MnSq values within the expected range (0.5 < MnSq < 1.7), suggesting the criteria contained an acceptable amount of variability; a reliability index of approximately 1.00 suggested that the criteria were reliably separated with a high degree of confidence. The rating scale Outfit MnSq statistics also fell within the 0.5–1.7 model fit limits; the “average measure” and “Rasch-Andrich thresholds” increased in magnitude as the rating scale categories increased, suggesting that core concepts with higher ratings were in fact meeting the criteria more convincingly than those with lower ratings. Adjusting expert ratings using the MFRM facets (e.g., rater severity) resulted in reorganization of core concepts rankings. Conclusion: This paper is a novel contribution to core concepts research and is intended to inform other disciplines seeking to develop, implement, and refine core concepts within the biomedical sciences and beyond

Using chemical, microbial and fluorescence techniques to understand contaminant sources and pathways to wetlands in a conservation site

Nutrients and faecal contaminants can enter wetland systems in a number of ways, with both biological and potentially human-health implications. In this study we used a combination of inorganic chemistry, dissolved organic matter (DOM) fluorescence and Escherichia coli and total coliform (TC) count techniques to study the sources and multiple pathways of contamination affecting a designated sand dune site of international conservation importance, surrounded by agricultural land. Analysis of stream samples, groundwater and dune slack wetlands revealed multiple input pathways. These included riverbank seepage, runoff events and percolation of nutrients from adjacent pasture into the groundwater, as well as some on-site sources. The combined techniques showed that off-site nutrient inputs into the sand dune system were primarily from fertilisers, revealed by high nitrate concentrations, and relatively low tryptophan-like fulvic-like ratios < 0.4 Raman units (R.U.). The E. coli and TC counts recorded across the site confirm a relatively minor source of bacterial and nutrient inputs from on-site grazers. Attenuation of the nutrient concentrations in streams, in groundwater and in run-off inputs occurs within the site, restoring healthier groundwater nutrient concentrations showing that contaminant filtration by the sand dunes provides a valuable ecosystem service. However, previous studies show that this input of nutrients has a clear adverse ecological impact

Efficient History Matching of a High Dimensional Individual-Based HIV Transmission Model

History matching is a model (pre-)calibration method that has been applied to computer models from a wide range of scientific disciplines. In this work we apply history matching to an individual-based epidemiological model of HIV that has 96 input and 50 output parameters, a model of much larger scale than others that have been calibrated before using this or similar methods. Apart from demonstrating that history matching can analyze models of this complexity, a central contribution of this work is that the history match is carried out using linear regression, a statistical tool that is elementary and easier to implement than the Gaussian process--based emulators that have previously been used. Furthermore, we address a practical difficulty with history matching, namely, the sampling of tiny, nonimplausible spaces, by introducing a sampling algorithm adjusted to the specific needs of this method. The effectiveness and simplicity of the history matching method presented here shows that it is a useful tool for the calibration of computationally expensive, high dimensional, individual-based models