Quantum Monte Carlo Study of Pairing Symmetry and Correlation in Iron-based Superconductors

We perform a systematic quantum Monte Carlo study of the pairing correlation in the $S_4$ symmetric microscopic model for iron-based superconductors. It is found that the pairing with an extensive s-wave symmetry robustly dominates over other pairings at low temperature in reasonable parameter region. The pairing susceptibility, the effective pairing interaction and the $(\pi,0)$antiferromagnetic correlation strongly increase as the on-site Coulomb interaction increases, indicating the importance of the effect of electron-electron correlation. Our non-biased numerical results provide a unified understanding of superconducting mechanism in iron-pnictides and iron-chalcogenides and demonstrate that the superconductivity is driven by strong electron-electron correlation effects.Comment: Accepted for publication as a Letter in Physical Review Letters, and more discussions are adde

The Abel-Zeilberger Algorithm

We use both Abel's lemma on summation by parts and Zeilberger's algorithm to find recurrence relations for definite summations. The role of Abel's lemma can be extended to the case of linear difference operators with polynomial coefficients. This approach can be used to verify and discover identities involving harmonic numbers and derangement numbers. As examples, we use the Abel-Zeilberger algorithm to prove the Paule-Schneider identities, the Apery-Schmidt-Strehl identity, Calkin's identity and some identities involving Fibonacci numbers.Comment: 18 page

Three-dimensional numerical study of flow characteristic and membrane fouling evolution in an enzymatic membrane reactor

In order to enhance the understanding of membrane fouling mechanism, the hydrodynamics of granular flow in a stirred enzymatic membrane reactor was numerically investigated in the present study. A three-dimensional Euler-Euler model, coupled with k-e mixture turbulence model and drag function for interphase momentum exchange, was applied to simulate the two-phase (fluid-solid) turbulent flow. Numerical simulations of single- or two-phase turbulent flow under various stirring speed were implemented. The numerical results coincide very well with some published experimental data. Results for the distributions of velocity, shear stress and turbulent kinetic energy were provided. Our results show that the increase of stirring speed could not only enlarge the circulation loops in the reactor, but it can also increase the shear stress on the membrane surface and accelerate the mixing process of granular materials. The time evolution of volumetric function of granular materials on the membrane surface has qualitatively explained the evolution of membrane fouling.Comment: 10 panges, 8 figure

Pairing in graphene: A quantum Monte Carlo study

To address the issue of electron correlation driven superconductivity in graphene, we perform a systematic quantum Monte Carlo study of the pairing correlation in the t-U-V Hubbard model on a honeycomb lattice. For V=0 and close to half filling, we find that pairing with d+id symmetry dominates pairing with extended-s symmetry. However, as the system size or the on-site Coulomb interaction increases, the long-range part of the d+id pairing correlation decreases and tends to vanish in the thermodynamic limit. An inclusion of nearest-neighbor interaction V, either repulsive or attractive, has a small effect on the extended-s pairing correlation, but strongly suppresses the d+id pairing correlation.Comment: 5 pages, 5 figure