Regensburg 2022 – wissenschaftliches Programm

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TT: Fachverband Tiefe Temperaturen

TT 21: Correlated Electrons: Poster Session

TT 21.28: Poster

Mittwoch, 7. September 2022, 15:00–18:00, P1

Calculating moments for many-electrons systems — •Elaheh Adibi and Erik Koch — Institute for Advanced Simulation, Forschungszentrum Jülich, 52425 Jülich, Germany

We present a technique for computing the moments ⟨ E^M⟩=Tr H^M of the many-electron spectrum. Taking the trace over a basis of Slater determinants |I⟩ and expressing the Hamiltonian in the same orbital basis, matrix elements ⟨ I|H^M|I⟩ can only be non-zero when the orbital indices of the creation operators are a permutation of those of the annihilation operators. Writing the permutations in cycle notation and realizing that the trace over a cycle with different orbital indices only depends on the number of descends, we can write the trace as a sum over products of Eulerian numbers times binomial factors involving the number of orbitals and electrons. For non-interacting electrons this further simplifies to a sum over Bell polynomials.