Exact thermal density functional theory for a model system: Correlation components and accuracy of the zero-temperature exchange-correlation approximation
Justin C Smith, Aurora Pribram-Jones, Kieron Burke
Thermal density functional theory calculations often use the Mermin-Kohn-Sham scheme, but employ ground-state approximations to the exchange-correlation (XC) free energy. In the simplest solvable nontrivial model, an asymmetric Hubbard dimer, we calculate the exact many-body energies and the exact Mermin-Kohn-Sham functionals for this system and extract the exact XC free energy. For moderate temperatures and weak correlation, we find this approximation to be excellent. We extract various exact free-energy correlation components and the exact adiabatic connection formula.
Density-functional theory for systems with noncollinear spin: orbital-dependent exchange-correlation functionals and their application to the Hubbard dimer
We present a first-principles investigation of the spin-ice state in Dy$_2$Ti$_2$O$_7$ using a magnetic source-free exchange and correlation functional, implemented in the Castep electronic-structure code. By comparing results from the conventional local spin-density approximation, we show that a spin-ice state in Dy$_2$Ti$_2$O$_7$ can be reliably obtained by removing the magnetic sources from the exchange and correlation contributions to the potential, and we contrast this against the computed ground states of other frustrated pyrochlore magnets.
Gross--Oliveira--Kohn (GOK) ensemble density-functional theory (GOK-DFT) is a time-\textit{independent} extension of density-functional theory (DFT) which allows to compute excited-state energies via the derivatives of the ensemble energy with respect to the ensemble weights. Contrary to the time-dependent version of DFT (TD-DFT), double excitations can be easily computed within GOK-DFT. However, to take full advantage of this formalism, one must have access to a \textit{weight-dependent} exchange-correlation functional in order to model the infamous ensemble derivative contribution to the exc…
In spin-density-functional theory (SDFT) for noncollinear magnetic materials, the Kohn-Sham system features exchange-correlation (xc) scalar potentials and magnetic fields. The significance of the xc magnetic fields is not very well explored; in particular, they can give rise to local torques on the magnetization, which are absent in standard local and semilocal approximations. Exact benchmark solutions for a five-site extended Hubbard lattice at half filling and in the presence of spin-orbit coupling are compared with SDFT results obtained using orbital-dependent exchange-only approximations.…
