Charge and Spin Density Waves in Jellium

Abstract Is the uniform electron gas unstable against charge and spin density waves (CDW's and SDW's) of infinitesimal amplitude, which break the translational symmetry of the Hamiltonian? Within density functional theory, a CDW of wavevector Q ≈︁ 1.1(2 k F ) appears at low densities. The local spin density approximation (LSDA) for exchange and correlation places the transition at r s ≈︁ 30, while inclusion of the next term in the gradient expansion suppresses the transition to densities as low as r s ≈︁ 200. The best estimate is that the CDW appears out of the uniform ferromagnetic phase of jellium at r s ≈︁ 70; this is also where Ceperley, in a recent calculation with correlated wave functions, found Wigner crystallization. Although no SDW in jellium is predicted within LSDA, the calculated uniform spin susceptibility diverges at r s ≈︁ 35, close to the highest density ( r s ≈︁ 26) at which Ceperley found ferromagnetism.