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TT: Fachverband Tiefe Temperaturen
TT 37: Correlated Electrons: Poster
TT 37.49: Poster
Mittwoch, 19. März 2025, 15:00–18:00, P4
Calculating Moments for Many-Electrons Systems — •Elaheh Adibi and Erik Koch — Peter Grünberg Institute and Institute for Advanced Simulation, Forschungszentrum Jülich, 52425 Jülich, Germany
We present a combinatorial approach to calculate the Mth moment of an N-electron system, defined as ⟨ EM⟩=Tr HM. Working in the basis of Slater determinants |α⟩ = ∏cαi†|0⟩, matrix elements ⟨α|HM|α⟩ may only be non-zero for terms where the orbital indices of the creation operators in HM are permutations of the orbital indices of the annihilators. The trace for a given permutation can then be evaluated combinatorially, without having to deal with the many-body Hilbert space explicitly. Since all permutations related by cyclic rotations give the same contribution, we classify them into groups and evaluate the trace only for a single group member. For the special case of all orbitals in the permutation being different, the calculation simplifies further, as in this irreducible case all permutations written in terms of cycles with a given number of descents give the same contribution to the moment. Relating the groups of permutations for the irreducible and the reducible terms allows us to efficiently evaluate the moments.
Keywords: many-body physics; moments