A v0-representability issue in lattice ensemble-DFT and its signature in lattice TDDFT

Abstract

We study a small Anderson-impurity cluster using lattice density functional methods, and try to determine the exact exchange-correlation (XC) potential via reverse engineering. In doing so we find singlettriplet degenerate interacting ground states which cannot be v0-represented in an ensemble-DFT sense. We also find that it is possible to represent a triplet ground state as a pure state, but not the singlet. We further investigate this behavior within time-dependent density-functional theory. Starting from a v0-representable ground state and entering the degeneracy region via a time-dependent perturbation, we determine via reverse-engineering the time-dependent XC potential for progressively slower perturbations. This analysis shows that, even in a constant external field, the XC potential must retain a time-oscillating pattern to ensure a density constant in time, a hint of the underlying representability issue in the ground state.

Density-functional theory on graphs

“…Such ensemble v-representability was also demonstrated for a coarse-grained version of continuum DFT [48; 49]. On the other hand, it has been stated recently by Rössler et al [50] that there are densities in P + M,N on simple lattice systems that are not ensemble v-representable, which would be in opposition to the theorem above. However, the claim rests on a numerical reverse-engineering procedure for finding a suitable potential v where uniqueness may have been assumed.…”

Special issue in honor of Eberhard K.U. Gross for his 65th birthday

“…In [24], Nagy develops a time-dependent functional theory that uses the density of electron pairs as basic variable. The problem of v 0 representability in lattice ensemble-DFT and its signature in lattice TDDFT is presented in [25]. Sangalli et al use non-equilibrium many-body perturbation theory, a powerful alternative to TDDFT, to study coherent and non-coherent exciton dynamics [26].…”