Berlin 2024 – wissenschaftliches Programm

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TT: Fachverband Tiefe Temperaturen

TT 80: Correlated Electrons: Poster

TT 80.44: Poster

Donnerstag, 21. März 2024, 15:00–18:00, Poster E

A Combinatorial Method for Calculating Moments of Many-Body Operators — •Elaheh Adibi and Erik Koch — Institute for Advanced Simulation, Forschungszentrum Jülich, 52425 Jülich, Germany

We introduce an approach for calculating the moments for many-electron systems defined as ⟨ E^M⟩=Tr H^M where H denotes the Hamiltonian in second quantization. Working in a basis of Slater determinants, |I⟩, matrix elements ⟨ I|H^M|I⟩ can only be non-zero if the orbital indices of the creation operators are a permutation of those of the annihilation operators. Classifying all permutations in terms of cycles enables us to calculate ∑_I⟨ I|H^M|I⟩ for different classes of cycles which is proportional to a binomial involving the number of orbitals and electrons. This binomial is then simply multiplied by the appropriate Eulerian number, which determines the number of permutations of a cycle with a given number of ascents.