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One-body reduced density-matrix functional theory in finite basis sets at elevated temperatures

Klaas J. H. Giesbertz, Michael Ruggenthaler

arXiv:1710.08805Physics ReportsFeb 12, 201930 citations

Density-functional theory formulated in terms of functional integrals

Gérald Faussurier

In a previous study, the author formulated the density functional theory in terms of functional integrals. It was valid at zero and finite temperature. It was possible to derive the Hohenberg and Kohn formulation at zero temperature and the Mermin formulation at finite temperature of the density functional theory, which states that the energy or the grand potential are functionals of the true density of the system considered. In particular, the Kohn and Sham equations are proven to appear naturally by performing a saddle-point evaluation of a specific functional integral. This result is valid at zero or finite temperature. Unfortunately, the expression of the grand potential given in our previous work differs from the usual expression found in the literature. In this short paper, we derive the common expression of the grand potential in the framework of the density functional theory by starting from the expression given in this previous work. This completes the formulation of the density functional theory using functional integrals. This work could be of interest to people working in the field of quantum Monte Carlo methods at finite temperature.In a previous study, the author formulated the density functional theory in terms of functional integrals. It was valid at zero and finite temperature. It was possible to derive the Hohenberg and Kohn formulation at zero temperature and the Mermin formulation at finite temperature of the density functional theory, which states that the energy or the grand potential are functionals of the true density of the system considered. In particular, the Kohn and Sham equations are proven to appear naturally by performing a saddle-point evaluation of a specific functional integral. This result is valid at zero or finite temperature. Unfortunately, the expression of the grand potential given in our previous work differs from the usual expression found in the literature. In this short paper, we derive the common expression of the grand potential in the framework of the density functional theory by starting from the expression given in this previous work. This completes the formulation of the density functional theory using functional integrals. This work could be of interest to people working in the field of quantum Monte Carlo methods at finite temperature.

AIP AdvancesJan 1, 20250 citations

Finite Temperature Scaling of the Non-interacting Free Energy Density Functional

James W. Dufty, Valentin V. Karasiev, Samuel B. Trickey

Bulletin of the American Physical SocietyMar 21, 20110 citations

Current Problems in Density Functional Theory

E. Zaremba

Springer eBooksJan 1, 19870 citations

Gradient corrections to the kinetic energy density functional of a two-dimensional Fermi gas at finite temperature

Brandon P. van Zyl, K. Berkane, K. Bencheikh +1 more

We examine the leading-order semiclassical gradient corrections to the noninteracting kinetic-energy density functional of a two-dimensional Fermi gas by applying the extended Thomas-Fermi theory at finite temperature. We find a nonzero von Weizs\"acker-like gradient correction, which in the high-temperature limit goes over to the functional form $(\ensuremath{\hbar}{}^{2}/24m)(\ensuremath{\nabla}\ensuremath{\rho}){}^{2}/\ensuremath{\rho}$. Our work provides a theoretical justification for the inclusion of gradient corrections in applications of density-functional theory to inhomogeneous two-dimensional Fermi systems at any finite temperature.We examine the leading-order semiclassical gradient corrections to the noninteracting kinetic-energy density functional of a two-dimensional Fermi gas by applying the extended Thomas-Fermi theory at finite temperature. We find a nonzero von Weizs\"acker-like gradient correction, which in the high-temperature limit goes over to the functional form $(\ensuremath{\hbar}{}^{2}/24m)(\ensuremath{\nabla}\ensuremath{\rho}){}^{2}/\ensuremath{\rho}$. Our work provides a theoretical justification for the inclusion of gradient corrections in applications of density-functional theory to inhomogeneous two-dimensional Fermi systems at any finite temperature.

arXiv:1012.0347Physical Review BMay 31, 20116 citations

Modern Density Functional Theory

Viraht Sahni

Springer tracts in modern physicsJan 1, 202247 citations

Density functional theory at finite temperatures

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