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TT: Fachverband Tiefe Temperaturen

TT 23: Correlated Electrons – Poster I

TT 23.21: Poster

Montag, 9. März 2026, 18:00–20:00, P1

Calculating Moments for Many-Electrons Systems — •Elaheh Adibi and Erik Koch — Peter Grünberg Institut, Forschungszentrum Jülich, 52425 Jülich, Germany

We describe an approach for computing the M^th moment of an N-electron system, defined as ⟨ E^M⟩=Tr H^M. Since the Hamiltonian H consists of pairs of creation-annihilation operators and the calculation is performed in the basis of Slater determinants {|I⟩}, the matrix element ⟨ I|H^M|I⟩ contributes to the moment only when the orbital indices of the creation operators form a permutation of those of the annihilation operators. Writing the permutations in cycle notation, the simplest contributions arise from permutations creating a single cycle in which all orbitals are different. These permutations are classified by their number of descents. Permutations with the same number of descents contribute equally to ∑_I⟨ I|H^M|I⟩. Since the number of permutations with the same number of descents is given by the Eulerian numbers, it suffices to compute the trace for one permutation and multiply the result by this number. In this way the trace can be evaluated combinatorially, without explicitly constructing the many-body Hilbert space. We are able to calculate the all other permutations with respect to these permutations. Finally, we present a recursive formula for the moment that is computationally efficient.

Keywords: many-body physics; moments