Events in Physics

In contemporary first-principles atomistic simulation, the augmentation of approximate density functionals with spatially or energetically localised corrections derived from model Hamiltonians is a common approach to improving their accuracy in more strongly interacting systems. This augmentation may take place on the level of subspace-projected density-matrices, as in the widely-used density-functional theory + Hubbard U (DFT+U) method, or at the level of subspace-projected Green's functions, as in DFT + dynamical mean-field theory (DFT+DMFT). In the context of DFT+U, the Hubbard U parameter is usually interpreted either as a measure of the curvature of the total-energy with respect to subspace occupancies, deemed erroneous and due for cancellation, or as the static limit of the screened Coulomb interaction. In the context of DFT+DMFT, the latter interpretation prevails, but in both cases a generalisation to dynamical, or non-adiabatic interaction parameters U seems admissible. It remains a somewhat open question, however, how essential it is to incorporate dynamical interaction parameters, both in order to match experiment and on fundamental grounds.

Here, I will develop a viewpoint from density-functional theory, starting from the definition of the Hubbard U as an energy curvature and seeking connections with the dynamical Coulomb interaction computed using the constrained random phase approximation and sometimes used in DFT+DMFT. I will introduce a recently-developed, inexpensive and very simplistic approach to computing model dynamical Hubbard U parameters, dubbed DFT+U(ω), developed to explore these connections. This is based on a readily-available combination of static density-functional linear-response theory for the Hubbard U and methods for the dielectric function, such as time-dependent density-functional theory (TDDFT), in which case we can move beyond the random phase approximation. I will discuss different strategies for solving the resulting non-Hamiltonian models, using either a local GW approximation to the self-energy, for which I will show some preliminary results on SrVO_3, or TDDFT.