Interpretations of ground-state symmetry breaking and strong correlation in wavefunction and density functional theories

Strong correlations within a symmetry-unbroken ground-state wavefunction can show up in approximate density functional theory as symmetry-broken spin-densities or total densities. They can arise from soft modes of fluctuations (sometimes collective excitations) such as spin-density or charge density waves at non-zero wavevector. Familiar examples are the unobservable but revealing symmetry breaking in stretched H₂ and the observable symmetry breaking in antiferromagnetic solids. The example discussed here is the static charge-density wave/Wigner crystal phase of a low density ( r_s = 69) jellium. Time-dependent density functional theory is used to show quantitatively that the static charge density wave is a soft plasmon. More precisely, the frequency of a related density fluctuation drops to zero, as found from the frequency moments of the spectral function. Our calculation is based on a recent constraint-based wavevector- and frequency-dependent jellium exchange-correlation kernel.<sup>1

1</sup> A. Ruzsinszky, N.K. Nepal, J.M. Pitarke, and J.P. Perdew, Physical Review B 101, 245135 (2020).