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تسجيل مستخدم جديدDerivation of the Density Functional via Effective Action
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Yi-Kuo Yu
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A rigorous derivation of the density functional in the Hohenberg-Kohn theory is presented. With no assumption regarding the magnitude of the electric coupling constant $e^2$ (or correlation), this work provides a firm basis for first-principles calculations. Using the auxiliary field method, in which $e^2$ need not be small, we show that the bosonic loop expansion of the exchange-correlation functional can be reorganized so as to be expressed entirely in terms of the Kohn-Sham single-particle orbitals and energies. The excitations of the many-particle system can be obtained within the same formalism. We also explicitly demonstrate at zero-temperature the single-particle limit, the weak-coupling limit of the energy functional, and its application to homogeneous electron gas.
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اقرأ أيضاً
A rigorous derivation of the density functional via the effective action in the Hohenberg-Kohn theory is outlined. Using the auxiliary field method, in which the electric coupling constant $e^2$ need not be small, we show that the loop expansion of t
he exchange-correlation functional can be reorganized so as to be expressed entirely in terms of the Kohn-Sham single-particle orbitals and energies.
We present a rigorous formulation of generalized Kohn-Sham density-functional theory. This provides a straightforward Kohn-Sham description of many-body systems based not only on particle-density but also on any other observable. We illustrate the fo
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Finite-temperature Kohn--Sham density-functional theory (KS-DFT) is a widely-used method in warm dense matter (WDM) simulations and diagnostics. Unfortunately, full KS-DFT-molecular dynamics models scale unfavourably with temperature and there remain
s uncertainty regarding the performance of existing approximate exchange-correlation (XC) functionals under WDM conditions. Of particular concern is the expected explicit dependence of the XC functional on temperature, which is absent from most approximations. Average-atom (AA) models, which significantly reduce the computational cost of KS-DFT calculations, have therefore become an integral part of WDM modelling. In this paper, we present a derivation of a first-principles AA model from the fully-interacting many-body Hamiltonian, carefully analysing the assumptions made and terms neglected in this reduction. We explore the impact of different choices within this model -- such as boundary conditions and XC functionals -- on common properties in WDM, for example equation-of-state data. Furthermore, drawing upon insights from ground-state KS-DFT, we speculate on likely sources of error in KS-AA models and possible strategies for mitigating against such errors.
Techniques based on $n$-particle irreducible effective actions can be used to study systems where perturbation theory does not apply. The main advantage, relative to other non-perturbative continuum methods, is that the hierarchy of integral equation
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