Odd-Frequency Density Waves: Non-Fermi-Liquid Metals with an Order Parameter

We consider states with a charge- or spin-density wave order parameter which is odd in frequency, so that the order parameter vanishes at zero frequency and there is a conventional Fermi surface. Such states break translational symmetry and, therefore, are not conventional Fermi liquids. In the odd-frequency spin-density wave case, there are Goldstone bosons and the low-energy spectrum is manifestly different from that of a Fermi liquid. We discuss a simple model which gives rise to such ordered states. The frequency-dependence of the gap leads to an unusual temperature dependence for various thermodynamic and transport properties, notably the resistivity.