Understanding plasmon dispersion in nearly free electron metals: Relevance of exact constraints for exchange-correlation kernels within time-dependent density functional theory

Nepal, Niraj K.; Adhikari, Santosh; Neupane, Bimal; Ruan, Shiqi; Neupane, Santosh; Ruzsinszky, Adrienn

doi:10.1103/physrevb.101.195137

Cited by 4 publications

(3 citation statements)

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“…It should be noted that [37], for metallic densities, the range of wave vectors relevant to the plasmon outside the electronhole continuum, 0 q < ∼k F , is different from the range relevant to the correlation energy, 0 < ∼q < ∼3k F . At much lower densities, the latter range is also relevant to the plasmon and charge-density wave.…”

Section: Discussionmentioning

confidence: 97%

“…In the range 0 q < ∼k F , the effective interaction 4π q 2 + f xc in Eq. ( 2) is dominated by 4π q 2 [37], so modest deviations of f xc from its RPA value 0, or better from the adiabatic local density approximation f xc (0,0), have almost negligible effect in that range, apart from emergent phenomena like the plasmon lifetime. Thus our applications test the kernel not only over a wide range of densities but also over a fairly wide range of q 2k F .…”

Section: Discussionmentioning

confidence: 99%

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Constraint-based wave vector and frequency dependent exchange-correlation kernel of the uniform electron gas

et al. 2020

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According to time-dependent density functional theory, the exact exchange-correlation kernel f xc (n, q, ω) for wave vector q and frequency ω determines not only the ground-state energy but also the excited-state energies/lifetimes and time-dependent linear density response of an electron gas of uniform density n = 3/(4π r 3 s ). Here we propose a parametrization of this function based upon the satisfaction of exact constraints. For the static (ω = 0) limit, we modify the model of Constantin and Pitarke to recover at small q the known second-order gradient expansion, and to correct its approach to the large q limit. For all ω at q = 0, we use the model of Gross, Kohn, and Iwamoto. A Cauchy integral extends this model to complex ω. Scaling relations are identified. We then combine these ingredients, damping out the ω dependence at large q. Away from q = 0 and ω = 0, the correlation contribution to the kernel becomes dominant over exchange, even at r s = 4. The resulting correlation energies for 1 r s 10 from integration over imaginary ω are essentially exact. The plasmon pole of the density response function is found by analytic continuation of f xc to ω just below the real axis, and the resulting plasmon lifetime at r s = 4 is found for q < k F . A static charge-density wave is found for r s > 69, and shown to be associated with softening of the plasmon mode.

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Section: Discussionmentioning

confidence: 97%

Section: Discussionmentioning

confidence: 99%

Constraint-based wave vector and frequency dependent exchange-correlation kernel of the uniform electron gas

et al. 2020

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“…[27], at wavevectors where the plasmon has not yet penetrated into the continuum of single particle-hole excitations. The dashed parts of the curves were computed here at all wavevectors using the frequency distribution (structure factor [20,21] or spectral function [22,34]) 𝑆 𝑞, 𝜔 = [−1/(𝜋𝑛)]𝐼𝑚𝜒 , 𝑞, 𝜔 > 0; 𝜒 , is the density response function at full coupling strength defined in Ref. [27).…”

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confidence: 99%

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

Perdew

Ruzsinszky

Sun

et al. 2021

Proc. Natl. Acad. Sci. U.S.A.

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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.

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Revealing quasi-excitations in the low-density homogeneous electron gas with model exchange–correlation kernels

Kaplan,

Ruzsinszky

2023

The Journal of Chemical Physics

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Time-dependent density functional theory within the linear response regime provides a solid mathematical framework to capture excitations. The accuracy of the theory, however, largely depends on the approximations for the exchange–correlation (xc) kernels. Away from the long-wavelength (or q = 0 short wave-vector) and zero-frequency (ω = 0) limit, the correlation contribution to the kernel becomes more relevant and dominant over exchange. The dielectric function, in principle, can encompass xc effects relevant to describe low-density physics. Furthermore, besides collective plasmon excitations, the dielectric function can reveal collective electron–hole excitations, often dubbed “ghost excitons.” Besides collective excitons, the physics of the low-density regime is rich, as exemplified by a static charge-density wave that was recently found for rs > 69, and was shown to be associated with softening of the plasmon mode. These excitations are seen to be present in much higher density 2D homogeneous electron gases of rs ≳ 4. In this work, we perform a thorough analysis with xc model kernels for excitations of various nature. The uniform electron gas, as a useful model of real metallic systems, is used as a platform for our analysis. We highlight the relevance of exact constraints as we display and explain screening and excitations in the low-density region.

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Understanding plasmon dispersion in nearly free electron metals: Relevance of exact constraints for exchange-correlation kernels within time-dependent density functional theory

Cited by 4 publications

References 48 publications

Constraint-based wave vector and frequency dependent exchange-correlation kernel of the uniform electron gas

Constraint-based wave vector and frequency dependent exchange-correlation kernel of the uniform electron gas

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

Revealing quasi-excitations in the low-density homogeneous electron gas with model exchange–correlation kernels

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