d_{xy}-Density wave in fermion-fermion cold atom mixtures

We study density wave instabilities in a doubly-degenerate Fermi-Fermi mixture with $SU(2)\times SU(2)$ symmetry on a square lattice. For sufficiently large on-site inter-species repulsion, when the two species of fermions are both at half-filling, two conventional ($s$-wave) number density waves are formed with a $\pi$-phase difference between them to minimize the inter-species repulsion. Upon moving one species away from half-filling, an unconventional density wave with $d_{xy}$-wave symmetry emerges. When both species are away from the vicinity of half-filling, superconducting instabilities dominate. We present results of a functional renormalization-group calculation that maps out the phase diagram at weak couplings. Also, we provide a simple explanation for the emergence of the $d_{xy}$-density wave phase based on a four-patch model. We find a robust and general mechanism for $d_{xy}$-density-wave formation that is related to the shape and size of the Fermi surfaces. The density imbalance between the two species of fermions in the vicinity of half-filling leads to phase-space discrepancy for different inter-species Umklapp couplings. Using a phase space argument for leading corrections in the one-loop renormalization group approach to fermions, we show that the phase-space discrepancy in our system causes opposite flows for the two leading intra-species Umklapp couplings and that this triggers the $d_{xy}$-density-wave instability.Comment: revised long version; 8 pages, 7 figure

Bose-Einstein condensation in an optical lattice

In this paper we develop an analytic expression for the critical temperature for a gas of ideal bosons in a combined harmonic lattice potential, relevant to current experiments using optical lattices. We give corrections to the critical temperature arising from effective mass modifications of the low energy spectrum, finite size effects and excited band states. We compute the critical temperature using numerical methods and compare to our analytic result. We study condensation in an optical lattice over a wide parameter regime and demonstrate that the critical temperature can be increased or reduced relative to the purely harmonic case by adjusting the harmonic trap frequency. We show that a simple numerical procedure based on a piecewise analytic density of states provides an accurate prediction for the critical temperature.Comment: 10 pages, 5 figure

EROSION AND THE LOSS OF SOIL PRODUCTIVITY ON THE TERRIL SOIL SERIES IN MINNESOTA

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Critical Entanglement for the Half-Filled Extended Hubbard Model

We study the ground state of the one-dimensional extended Hubbard model at half-filling using the entanglement entropy calculated by Density Matrix Renormalization Group (DMRG) techniques. We apply a novel curve fitting and scaling method to accurately identify a $2^{nd}$ order critical point as well as a Berezinskii-Kosterlitz-Thouless (BKT) critical point. Using open boundary conditions and medium-sized lattices with very small truncation errors, we are able to achieve similar accuracy to previous authors. We also report observations of finite-size and boundary effects that can be remedied with careful pinning.Comment: 10 pages, 12 figure

The Realization and Dectection of Weyl Semimetals and Chiral Anomaly in Cold Atomic Systems

In this work, we describe a method to realize 3D Weyl semimetal by coupling multilayers of honeycomb optical lattice in the presence of a pair of Raman lasers. The Raman lasers render each isolated honeycomb layer a Chern insulator. With finite interlayer coupling, the bulk gap of the system closes at certain out-of-plane momenta due to Raman assisted tunnelling and result in the Weyl semimetal phase. Using experimentally relevant parameters, we show that both one and two pairs of Weyl points can be realized by tuning the interlayer coupling strength. We suggest that Landau-Zener tunnelling can be used to detect Weyl points and show that the transition probability increases dramatically when Weyl point emerges. The realization of chiral anomaly by using a magnetic field gradient is also discussed.Comment: 6 pages, 5 figures. Comments are welcom