We give a general definition of unpolarized light that rests on invariance properties rather than specific values of second-order field correlations or, equivalently, the Stokes parameters. It turns out that to require invariance with respect to rotation around the propagation axis and symmetry with respect to left- and right-handed circular polarization is not sufficient to fully characterize completely unpolarized light, such as natural light. Actually, a third requirement demanding invariance with respect to phase retardation is needed. Depending on whether it is satisfied or not, we speak of type I or type II unpolarized light, and we specify the general form of both classical distribution functions and density operators consistent with the respective conditions. \textcopyright{} 1996 The American Physical Society.
Coulomb repulsion between electrons moving on a frustrated lattice can give rise, at simple commensurate electronic densities, to exotic insulating phases of matter. Such a phenomenon is illustrated using an extended $t\text{\ensuremath{-}}J$ model on a planar pyrochlore lattice for which the work on the quarter-filled case [D. Poilblanc et al., Phys. Rev. B 75, 220503 (2007)] is complemented and extended to
1∕8 and
3∕8 fillings. The location of the metal-insulator transition as a function of the Coulomb repulsion is shown to depend strongly on the sign of the hopping. Quite generally, the metal-insulator transition is characterized by lattice symmetry breaking but the nature of the insulating Mott state is more complex than a simple charge density wave. Indeed, in the limit of large Coulomb repulsion, the physics can be described in the framework of (extended) quantum fully packed loop or dimer models carrying extra spin degrees of freedom. Various diagonal and off-diagonal plaquette correlation functions are computed and the low-energy spectra are analyzed in detail in order to characterize the nature of the insulating phases. We provide evidence that, as for an electronic density of
n=1∕2 (quarter filling), the system at
n=1∕4 or
n=3∕4 exhibits also plaquette order by forming a (lattice rotationally invariant) resonant singlet pair crystal, although with a quadrupling of the lattice unit cell (instead of a doubling for
n=1∕2) and a fourfold degenerate ground state. Interestingly, qualitative differences with the bosonic analog (e.g., known to exhibit columnar order at
n=1∕4) emphasize the important role of the spin degrees of freedom in, e.g., stabilizing plaquette phases with respect to rotational symmetry-breaking phases.
Today, most applications of time-dependent density-functional theory use adiabatic exchange-correlation (XC) potentials that do not take into account nonlocal temporal effects. Incorporating such ``memory'' terms into XC potentials is complicated by the constraint that the derived force and torque densities must integrate to zero at every instance. This requirement can be met by deriving the potentials from an XC action that is both rotationally and translationally invariant, i.e., Galilean invariant (GI). We develop a class of simple but flexible forms for an action that respect these constraints. The basic idea is to formulate the action in terms of the Eularian-Lagrangian transformation metric tensor, which is itself GI. The general form of the XC potentials in this class is then derived, and the linear response limit is derived as well.