arXiv:1208.4705

Reduced density matrix functional theory at finite temperature. II. Application to the electron gas: Exchange only

Tim Baldsiefen, F. G. Eich, Eberhard K. U. Gross

Published Aug 23, 2012• 4 citations

Abstract

Using the newly introduced theory of finite-temperature reduced density matrix functional theory, we apply the first-order approximation to the homogeneous electron gas. We consider both collinear spin states as well as symmetry broken states describing planar spin spirals and investigate the magnetic phase diagram as well as the temperature-dependence of the single particle spectra.

DOI: 10.48550/arxiv.1208.4705

Related papers

Reduced density matrix functional theory at finite temperature. III. Application to the electron gas: Correlation effects

Tim Baldsiefen, Eberhard K. U. Gross

Based on our derivation of finite temperature reduced density matrix functional theory and the discussion of the performance of its first-order functional this work presents several different correlation-energy functionals and applies them to the homogeneous electron gas. The zero temperature limits of the correlation-energy and the momentum distributions are investigated and the magnetic phase diagrams in collinear spin configuration are discussed.

arXiv:1208.4707Aug 23, 20124 citations

Exchange-correlation approximations for reduced-density-matrix-functional theory at finite temperature: Capturing magnetic phase transitions in the homogeneous electron gas

Tim Baldsiefen, Attila Cangi, F. G. Eich +1 more

We derive an intrinsically temperature-dependent approximation to the correlation grand potential for many-electron systems in thermodynamical equilibrium in the context of finite-temperature reduced-density-matrix-functional theory (FT-RDMFT). We demonstrate its accuracy by calculating the magnetic phase diagram of the homogeneous electron gas. We compare it to known limits from highly accurate quantum Monte Carlo calculations as well as to phase diagrams obtained within existing exchange-correlation approximations from density functional theory and zero-temperature RDMFT.

Physical Review ADec 18, 20178 citations

Reduced density matrix functional theory at finite temperature

Tim Baldsiefen

In this dissertation we present a new ab-initio functional theory (FT-RDMFT) to describe many-particle quantum systems at finite temperature. The work can be divided roughly into three parts. In the first part, we lay the mathematical foundation for FT-RDMFT. In the second part, we develop analytical and numerical methods to approximate and minimize the exact functional. We conclude by applying FT-RDMFT to the important model system of the homogeneous electron gas.

Jan 1, 20125 citations

Performance of one-body reduced density-matrix functionals for the homogeneous electron gas

Nektarios N. Lathiotakis, N. Helbig, Eberhard K. U. Gross

The subject of this study is the exchange-correlation-energy functional of reduced density-matrix functional theory. Approximations of this functional are tested by applying them to the homogeneous electron gas. We find that two approximations recently proposed by Gritsenko et al., [J. Chem. Phys. 122, 204102 (2005)] yield considerably better correlation energies and momentum distributions than previously known functionals. We introduce modifications to these functionals, which, by construction, reproduce the exact correlation energy of the homogeneous electron gas.

arXiv:cond-mat/0605531Physical Review BMay 21, 200759 citations

Thermodynamic extension of density-functional theory. II. Finite-temperature ensemble spin-density functional theory

Robert Balawender, A. Holas

The formalism developed in the first paper of the series [arXiv:0901.1060] is applied to two thermodynamic systems: (i) of three global observables (the energy, the total electron number and the spin number), (ii) of one global observable (the internal electron energy) and two local (position-dependent) observables (the total electron density and the spin density). The two-component potential of the many-electron system of interest is constructed of a scalar external potential and a collinear magnetic field (coupled only with the spin operator). Various equilibrium characteristics of two systems are defined and investigated. Conditions for the equivalence between two systems (the same equilibrium density matrix demanded) are derived and thoroughly discussed. The applicability of the Hohenberg-Kohn theorem is extended to the thermodynamic spin-density functional theory. Obtained results provide a rigorous mathematical foundation for future derivation of the zero-temperature limit of this theory and determination of its chemical reactivity indices.

arXiv:0904.3990Apr 25, 20095 citations

Noncollinear spin-spiral phase for the uniform electron gas within reduced-density-matrix-functional theory

F. G. Eich, Stefan Kurth, César R. Proetto +2 more

The noncollinear spin-spiral density wave of the uniform electron gas is studied in the framework of reduced-density-matrix-functional theory. For the Hartree-Fock approximation, which can be obtained as a limiting case of reduced-density-matrix-functional theory, Overhauser showed a long-time ago that the paramagnetic state of the electron gas is unstable with respect to the formation of charge- or spin-density waves. Here we not only present a detailed numerical investigation of the spin-spiral density wave in the Hartree-Fock approximation but also investigate the effects of correlations on the spin-spiral density wave instability by means of a recently proposed density-matrix functional.

arXiv:0910.0534Physical Review BJan 29, 201011 citations