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, which are sometimes observable. They can arise from soft modes of fluctuations (sometimes collective excitations) such as spin-density or charge-density waves at nonzero wavevector. In this sense, an approximate density functional for exchange and correlation that breaks symmetry can be more revealing (albeit less accurate) than an exact functional that does not. The examples discussed here include the stretched H₂ molecule, antiferromagnetic solids, and the static charge-density wave/Wigner crystal phase of a low-density 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, calculated from a recent constraint-based wavevector- and frequency-dependent jellium exchange-correlation kernel.

对称性完整的基态波函数内的强相关性可以在近似密度泛函理论中显示为对称性破坏的自旋密度或总密度，这有时是可观察到的。它们可能来自波动的软模式（有时是集体激发），例如非零波矢量的自旋密度或电荷密度波。从这个意义上说，打破对称性的交换和相关性的近似密度泛函比没有对称性的精确泛函更具启发性（尽管不太准确）。这里讨论的例子包括拉伸的 H ₂分子、反铁磁固体和低密度凝胶的静电荷密度波/维格纳晶相。时间相关的密度泛函理论用于定量地表明静电荷密度波是一种软等离子体。更准确地说，相关密度波动的频率下降到零，如从谱函数的频矩中发现的那样，从最近的基于约束的波矢量和频率相关的 jellium 交换相关核计算得出。