Time-dependent density-functional theory for strongly correlated electrons

One of the most used methods in condensed matter theory and quantum chemistry for the description of matter properties is Time-dependent density-functional theory (TDDFT), an alternative formalism to wave function methods which uses the time-dependent electronic density for the determination of any quantum average of an electronic system. The usual approach in TDDFT is by means a noninteracting system, where all the interaction e ects are encoded in an e ective one-body potential that exactly reproduces the time-dependent density of any interacting system. The e ective potential is called the exchange-correlation (xc) potential. For the calculation of the excited states in TDDFT, one needs the knowledge of the xc potential and its functional derivative with respect to the density, which is known as the xc kernel. For practical applications, both the xc potential and the xc kernel needs to be approximated. In the last years, better approximations for the xc potential and kernel have been constructed, but it turns out that the usual approximations fail for the description of strongly correlated systems. Recently, a new type of density functionals, the strictly correlated electrons (SCE) formalism [1 3] have been constructed with the aim to describe the physics of strongly correlated systems, but not tested so far for the obtaining of excitation energies. One way to gain insight and test the performance of the density functionals is to compare them against exact expressions obtained from exactly solvable systems. In this work, we construct such strongly correlated systems, and we solve them exactly for the subsequent comparison with the predictions provided by the SCE density functionals. The comparison of the results, therefore, will provide insights of the applicability of this kind of density functionals, establishing in this way its range of validity.