We study the instability of the metallic state toward the formation of a different ground state in graphene doped near the van Hove singularity. The system is described by the Hubbard model and a field theoretical approach is used to calculate the charge and spin susceptibility. We find that for repulsive interactions, within the random phase approximation, there is a competition between ferromagnetism and the spin-density wave (SDW). It turns out that a SDW with a triangular geometry is more favorable when the Hubbard parameter is above the critical value U c (T ), which depends on the temperature T , even if there are small variations in the doping. Our results can be verified by angle-resolved photoemission spectroscopy or neutron scattering experiments in highly doped graphene.
We investigate two theoretical pseudomagnon-based models for a bilayer quantum Hall system ͑BQHS͒ at total filling factor t = 1. We find a unifying framework which elucidates the different approximations that are made. We also consider the effect of an in-plane magnetic field in BQHSs at t = 1, by deriving an equation for the ground-state energy from the underlying microscopic physics. Although this equation is derived for small in-plane fields, its predictions agree with recent experimental findings at stronger in-plane fields, for low electron densities. We also take into account finite-temperature effects by means of a renormalization group analysis, and find that they are small at the temperatures that were investigated experimentally.
We derive and discuss an experimentally realistic model describing ultracold atoms in an optical lattice including a commensurate, but staggered, Zeeman field. The resulting band structure is quite exotic; fermions in the third band have an unusual rounded picture-frame Fermi surface (essentially two concentric squircles), leading to imperfect nesting. We develop a generalized SO(3, 1) × SO(3, 1) theory describing the spin and charge degrees of freedom simultaneously, and show that the system can develop a coupled spin-charge-density wave order. This ordering is absent in studies of the Hubbard model that treat spin and charge density separately.Introduction Ultracold atoms in optical lattices have recently emerged as a class of condensed matter systems, where the properties of the many-body Hamiltonian are under exquisite experimental control. Interfering laser beams in one, two or three dimensions (D) create standing waves: nearly perfect optical lattices for atoms with lattice spacing and topology set by the laser geometry and wavelength [1]. Optical lattices not only allow for the implementation of different lattice models without defects, but also open a wide range of possibilities to manipulate the parameters of the model describing ultracold bosons, fermions, or mixtures thereof. For example, the hopping parameters, local chemical potential, and often even the interaction strength can be tuned at will.Most optical lattice experiments use atoms in a single state [2], however, some experiments study mixtures of atoms in two or more atomic "spin" states, each of which can experience different lattice potentials [3][4][5]. We derive a lattice model, equally applicable to bosons and fermions, with an effective Zeeman magnetic field including a term alternating in sign on a site-by-site basis [6]. In condensed matter systems, the Zeeman field couples strongly to electrons near the Fermi surface [7], and in more orchidaceous situations, it breaks local timereversal invariance in topological insulators [8,9].For particles with two spin states, our lattice model has four low-energy bands, and the third is shaped as a squarish, deformed, Mexican hat for a wide range of system parameters. By filling the system with fermions, we obtain a peculiar Fermi surface, consisting of the boundaries of a squarish ring, essentially two concentric squircles [10]. The particular shape of the Fermi surface suggests that nesting effects should be expected. To account for interactions, we develop an SO(3, 1) × SO(3, 1) description of the charge and spin degrees of freedom. Imperfect nesting along the diagonal connecting corners of the Fermisurface gives rise to a coupled spin-charge-density wave (SCDW) instability at a critical interaction strength U c . We calculate the imaginary part of the trace of the random phase approximation (RPA) susceptibility to study the collective excitations of the system. At the interac-
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