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

Tim Baldsiefen, E. K. U. Gross|arXiv (Cornell University)|Aug 23, 2012

Advanced Chemical Physics Studies3 citations

TL;DR

This paper develops and applies finite-temperature reduced density matrix functional theory (FT-RDMFT) to the homogeneous electron gas, introducing a new correlation-energy functional (BOW) that accurately reproduces Monte Carlo correlation energies across all densities and spin polarizations. It further proposes a truly temperature-dependent functional (κ-TIE) that yields a qualitatively correct magnetic phase diagram with a smooth transition to the paramagnetic phase, overcoming the unphysical first-order transitions of prior functionals.

ABSTRACT

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.

Motivation & Objective

• To develop accurate finite-temperature correlation-energy functionals within reduced density matrix functional theory (FT-RDMFT) for the homogeneous electron gas (HEG).
• To overcome the failure of standard spin-channel-separable functionals in describing spin-polarized HEG systems across all polarizations and densities.
• To construct a functional that reproduces both the correlation energy and momentum distribution of the HEG accurately at zero temperature.
• To derive a truly temperature-dependent functional that correctly describes the evolution of magnetic phases with temperature.
• To provide a foundation for future applications of FT-RDMFT to real solids by validating functionals against high-accuracy Monte Carlo data.

Proposed method

• Derives a new zero-temperature correlation functional (BOW) based on exact limits of the RPA polarization propagator and Monte Carlo data, ensuring accurate correlation energies for arbitrary spin polarization.
• Proposes a temperature-dependent functional (κ-TIE) by extending the BOW functional with a momentum- and temperature-dependent correction term derived from the RPA polarization function.
• Uses the grand potential functional formalism in FT-RDMFT, where the 1RDM is the fundamental variable, and the universal functional F[γ] is decomposed into non-interacting and correlation contributions.
• Applies perturbative methods to derive the temperature dependence of the correlation functional, ensuring consistency with thermodynamic constraints.
• Employs the spectral representation of the 1RDM with natural orbitals and occupation numbers to describe electronic correlations beyond standard DFT.
• Validates functionals against high-accuracy quantum Monte Carlo results for the HEG at various densities and temperatures, focusing on correlation energy and momentum distribution.

Experimental results

Research questions

• RQ1 Can a finite-temperature correlation functional in RDMFT accurately describe the correlation energy of the homogeneous electron gas across all densities and spin polarizations?
• RQ2 Why do standard spin-channel-separable functionals fail to describe the HEG for arbitrary polarization, and how can this be corrected?
• RQ3 Can a functional be constructed that simultaneously reproduces the correct correlation energy and momentum distribution in the HEG at zero temperature?
• RQ4 How can a truly temperature-dependent correlation functional be derived within FT-RDMFT that yields a physically reasonable magnetic phase diagram?
• RQ5 What role do momentum distribution-dependent corrections play in improving the description of correlation effects in finite-temperature RDMFT?

Key findings

• The BOW functional reproduces the correlation energy of the 2D and 3D homogeneous electron gas with unprecedented accuracy across all densities and spin polarizations, matching high-accuracy quantum Monte Carlo data.
• The BOW functional correctly captures the qualitative behavior of the momentum distribution, including the correct Fermi surface structure, unlike previous RDMFT functionals.
• The κ-TIE functional, a temperature-dependent extension of the BOW functional, eliminates unphysical first-order phase transitions and yields a smooth evolution from ferromagnetic to paramagnetic phases with increasing temperature.
• The critical density for the ferromagnetic transition is significantly reduced in the κ-TIE functional compared to earlier functionals, bringing it into better agreement with physical expectations.
• The functional parameters for the κ-TIE functional (κ = 3.2, c = 0.24) were optimized to reproduce Monte Carlo correlation energies and momentum distributions across the full density range.
• The study demonstrates that standard DFT-based correlation functionals lead to uncorrelated momentum distributions in FT-RDMFT, highlighting the need for momentum distribution-dependent functionals in finite-temperature RDMFT.