Hartree-Fock state for the two-dimensional electron gas at ν=1 / 2: Analytic solution, dynamics, and correlation energy

The charge-density wave (CDW) Hartree-Fock state at half-filling and with half an electron per unit cell is examined. First, an exact solution in terms of Bloch-like states is presented. Using this solution we discuss the dynamics near half-filling and show the mass to diverge logarithmically as this filling is approached. We also show how a uniform density state may be constructed from a linear combination of two degenerate solutions. Finally we show the second-order correction to the energy to be an order of magnitude larger than that for competing CDW solutions with one electron per unit cell.