The adiabatic strictly-correlated-electrons functional: kernel and exact properties

Lani, Giovanna; Marino, Simone Di; Gerolin, Augusto; Leeuwen, Robert van; Gori‐Giorgi, Paola

doi:10.1039/c6cp00339g

Cited by 15 publications

(28 citation statements)

References 52 publications

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“…This is the case for densities ρ 1,2 in (39) which both decay exponentially (or faster). Such a divergence of ω(x) makes the interpretation of the expansion of v λ less straightforward: for what just stated in (42), at large distances, its asymptotic expansion reads…”

Section: Numerical Results For Selected Densitiesmentioning

confidence: 99%

“…The frequency function ω(x) is an implicit functional of the density, via the co-motion function and its derivative. Even for 2 electrons in D = 1, computing the functional derivatives of f (x) can be delicate, as it changes sign when N e (s) = 1: perturbing the density in this point implies taking into account a step function, for which the chain rule does not apply (see Appendix in [42] for further details).…”

Section: B Explicit Expressionmentioning

confidence: 99%

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Functional derivative of the zero-point-energy functional from the strong-interaction limit of density-functional theory

Grossi¹,

Seidl²,

Gori‐Giorgi³

et al. 2019

Phys. Rev. A

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We derive an explicit expression for the functional derivative of the subleading term in the strong interaction limit expansion of the generalized Levy-Lieb functional for the special case of two electrons in one dimension. The expression is derived from the zero point energy (ZPE) functional, which is valid if the quantum state reduces to strongly correlated electrons in the strong coupling limit. The explicit expression is confirmed numerically and respects the relevant sum-rule. We also show that the ZPE potential is able to generate a bond mid-point peak for homo-nuclear dissociation and is properly of purely kinetic origin. Unfortunately, the ZPE diverges for Coulomb systems, whereas the exact peaks should be finite.

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Section: Numerical Results For Selected Densitiesmentioning

confidence: 99%

Section: B Explicit Expressionmentioning

confidence: 99%

Functional derivative of the zero-point-energy functional from the strong-interaction limit of density-functional theory

Grossi¹,

Seidl²,

Gori‐Giorgi³

et al. 2019

Phys. Rev. A

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“…Given these generalities, we were motivated to find an analytical (and at least semi-quantitatively correct) frequency-dependent kernel common for systems of different sizes and geometries. It is also important to mention that in constructing an accurate analytical kernel, one also needs to take into account known constraints that come from many-body theory, such as the generalized translational invariance and the zero-force theorem (see [20] for some discussion in this regard).…”

Section: Numerical Resultsmentioning

confidence: 99%

Towards TDDFT for Strongly Correlated Materials

2016

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Abstract:We present some details of our recently-proposed Time-Dependent Density-Functional Theory (TDDFT) for strongly-correlated materials in which the exchange-correlation (XC) kernel is derived from the charge susceptibility obtained using Dynamical Mean-Field Theory (the TDDFT + DMFT approach). We proceed with deriving the expression for the XC kernel for the one-band Hubbard model by solving DMFT equations via two approaches, the Hirsch-Fye Quantum Monte Carlo (HF-QMC) and an approximate low-cost perturbation theory approach, and demonstrate that the latter gives results that are comparable to the exact HF-QMC solution. Furthermore, through a variety of applications, we propose a simple analytical formula for the XC kernel. Additionally, we use the exact and approximate kernels to examine the nonhomogeneous ultrafast response of two systems: a one-band Hubbard model and a Mott insulator YTiO 3 . We show that the frequency dependence of the kernel, i.e., memory effects, is important for dynamics at the femtosecond timescale. We also conclude that strong correlations lead to the presence of beats in the time-dependent electric conductivity in YTiO 3 , a feature that could be tested experimentally and that could help validate the few approximations used in our formulation. We conclude by proposing an algorithm for the generalization of the theory to non-linear response.

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“…In recent work [5] an approximate kernel was derived within the framework of so-called strictly correlate electrons (SCE). This is a ground state DFT formalism that becomes exact in the limit of very large two-body interactions.…”

Section: Introductionmentioning

confidence: 99%

“…This socalled adiabatic SCE (ASCE) kernel was shown to have a number of desirable features. It was shown to obey the so-called zero-force theorem [2,6] and it was shown that in the case of molecular dissociation it exhibits an exponential growth with the bond distance [5]. The kernel therefore displays a very non-local spatial behavior that has the potential to cure the deficiency of the ALDA kernel for molecular dissociation.…”

Section: Introductionmentioning

confidence: 99%

Strictly-correlated-electron approach to excitation energies of dissociating molecules

2019

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In this work we consider a numerically solvable model of a two-electron diatomic molecule to study a recently proposed approximation based on the density-functional theory of so-called strictly correlated electrons (SCE). We map out the full two-particle wave function for a wide range of bond distances and interaction strengths and obtain analytic results for the two-particle states and eigenenergies in various limits of strong and weak interactions, and in the limit of large bond distance. We then study the so-called Hartree-exchange-correlation (Hxc) kernel of time-dependent density functional theory which is a key ingredient in calculating excitation energies. We study an approximation based on adiabatic SCE (ASCE) theory which was shown to display a particular feature of the exact Hxc-kernel, namely a spatial divergence as function of the bond distance. This makes the ASCE kernel a candidate for correcting a notorious failure of the commonly used adiabatic local density approximation (ALDA) in the calculation of excitation energies of dissociating molecules. Unlike the ALDA, we obtain non-zero excitation energies from the ASCE kernel in the dissociation regime but they do not correspond to those of the true spectrum unless the interaction strength is taken to be very large such that the SCE theory has the right regime of validity, in which case the excitation energies become exact and represent the so-called zero point oscillations of the strictly correlated electrons. The commonly studied physical dissociation regime, namely large molecular separation at intermediate interaction strength, therefore remains a challenge for density functional approximations based on SCE theory. arXiv:1901.05266v1 [cond-mat.str-el]

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The adiabatic strictly-correlated-electrons functional: kernel and exact properties

Cited by 15 publications

References 52 publications

Functional derivative of the zero-point-energy functional from the strong-interaction limit of density-functional theory

Functional derivative of the zero-point-energy functional from the strong-interaction limit of density-functional theory

Towards TDDFT for Strongly Correlated Materials

Strictly-correlated-electron approach to excitation energies of dissociating molecules

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