Synopsis: Theory tackles strong interactions
In density-functional theory, which is perhaps the most widely used technique to study quantum many-particle systems, ground-state properties are calculated by minimizing an energy functional with respect to the particle density. In the Kohn-Sham approach, first formulated in 1965, this is done under the assumption that kinetic energy dominates. The approach works well in many scenarios, but as expected, runs into difficulty where particle-particle interactions play a more prominent role.
In a paper in Physical Review Letters, Paola Gori-Giorgi at the CNRS in Paris, France, Michael Seidl at the University of Regensburg in Germany, and Giovanni Vignale at the University of Missouri in the US introduce an alternative method within density-functional theory to deal with these strongly correlated systems. In essence, they minimize the expectation value of the electron-electron interaction energy instead of that of the kinetic energy (as done in the Kohn-Sham approach).
This technique allows Gori-Giorgi et al. to specifically study ground-state properties of strongly correlated electron systems. One such example that has frustrated condensed matter theorists for years is the Wigner crystal, which is formed when interactions solidify a two-dimensional electron gas into a lattice. One expects the authors’ approach to work with a host of such low-density many-particle scenarios, such as quantum dots. – Sami Mitra