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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
s that must be solved truncates at the level of the action, and no additional approximations are needed. The main problem with the method is renormalization, which until now could only be done at the lowest ($n$=2) level. In this paper we show how to obtain renormalized results from an $n$-particle irreducible effective action at any order. We consider a symmetric scalar theory with quartic coupling in four dimensions and show that the 4 loop 4-particle-irreducible calculation can be renormalized using a renormalization group method. The calculation involves one bare mass and one bare coupling constant which are introduced at the level of the Lagrangian, and cannot be done using any known method by introducing counterterms.
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