Interpretations of ground-state symmetry breaking and strong correlation in wavefunction and density functional theories
Interpretations of ground-state symmetry breaking and strong correlation in wavefunction and density functional theories
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DOI：
10.1073/pnas.2017850118
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发表时间：
2020-07
期刊：
影响因子：
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通讯作者：
J. Perdew;A. Ruzsinszky;Jianwei Sun;N. Nepal;Aaron D. Kaplan
中科院分区：
文献类型：
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作者：
J. Perdew;A. Ruzsinszky;Jianwei Sun;N. Nepal;Aaron D. Kaplan
意义量子力学系统的基态是哈密顿量的最低能量特征态。在孤立的情况下，它永远保持不变，其对称性由哈密顿量决定。但对称性破缺的近本征态可以持续很长时间，即使在人类测量的尺度上也是如此。在密度泛函计算中，电子密度或自旋密度对称性破缺的出现可以揭示存在于对称未破缺波函数中的电子之间的强相关性。当波状波动降至零频率时，就会出现对称性破缺。本文给出的例子包括拉伸氢分子、固体中的反铁磁性和低密度凝胶中的静态电荷密度波，定量地证明了它是零频率等离子体波。在近似密度泛函理论中，对称未破缺的基态波函数中的强相关性可以表现为对称破缺的自旋密度或总密度，有时可以观察到。它们可以产生于波动的软模式（有时是集体激励），如非零波矢量上的自旋密度波或电荷密度波。从这个意义上说，用于交换和关联的近似密度泛函会打破对称，这可能比不打破对称的精确泛函更能揭示问题（尽管不那么精确）。这里讨论的例子包括拉伸H2分子，反铁磁性固体，以及低密度凝胶的静态电荷密度波/Wigner晶体相。利用时变密度泛函理论定量地证明了静态电荷密度波是软等离激元。更准确地说，相关密度波动的频率降至零，这是根据最近基于约束的波长和频率相关的凝胶交换相关核计算得出的频谱函数的频率矩。
Significance The ground state of a quantum mechanical system is the lowest-energy eigenstate of the Hamiltonian. In isolation, it persists unchanged forever, with symmetries dictated by those of the Hamiltonian. But near-eigenstates of broken symmetry can persist for long times, even on the scale of human measurement. The appearance of broken symmetries of the electron density or spin density in a density functional calculation can reveal strong correlations among the electrons that are present in a symmetry-unbroken wavefunction. Symmetry breaking can arise when a wave-like fluctuation drops to zero frequency. The presented examples are the stretched hydrogen molecule, antiferromagnetism in solids, and the static charge-density wave in a low-density jellium, which is shown quantitatively to be a zero-frequency plasma wave. 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.