Approximate energy functionals for one-body reduced density matrix functional theory from many-body perturbation theory

Density functionals from many-body perturbation theory: the band gap for semiconductors and insulators.

Theoretically the Kohn-Sham band gap differs from the exact quasiparticle energy gap by the derivative discontinuity of the exchange-correlation functional. In practice for semiconductors and insulators the band gap calculated within any local or semilocal density approximations underestimates severely the experimental energy gap. On the other hand, calculations with an "exact" exchange potenti...

Avoiding the 4-index transformation in one-body reduced density matrix functional calculations for separable functionals.

One of the major computational bottlenecks in one-body reduced density matrix (1RDM) functional theory is the evaluation of approximate 1RDM functionals and their derivatives. The reason is that more advanced approximate functionals are almost exclusively defined in the natural orbital basis, so a 4-index transformation of the two-electron integrals appears to be unavoidable. I will show that t...

Time-Dependent One-Body Reduced Density Matrix Functional Theory Adiabatic Approximations and Beyond

Quantum Many–Body Problems and Perturbation Theory

We show that the existence of algebraic forms of exactly-solvable A−B− C−D and G2, F4 Olshanetsky-Perelomov Hamiltonians allow to develop the algebraic perturbation theory, where corrections are computed by pure algebraic means. A classification of perturbations leading to such a perturbation theory based on representation theory of Lie algebras is given. In particular, this scheme admits an ex...

Many-Body Perturbation Theory: The GW Approximation

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