SAMOP 2023 – scientific programme

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QI: Fachverband Quanteninformation

QI 20: Concepts and Methods II

QI 20.6: Talk

Wednesday, March 8, 2023, 15:45–16:00, B302

Computational Complexity in Functional Theory — •Lukas Kienesberger, Julia Liebert, and Christian Schilling — University of Munich (LMU), Munich, Germany

Using tools from quantum information theory, we investigate the computational complexity of calculating the universal energy functional in functional theories. Firstly, we prove for the two-fermion Hubbard model that the space of density matrices constituting the functional's domain decomposes into exponentially many regions, separated by submanifolds where the functional fails to be analytic. As our second main result, we show that determining the functional itself on those cells is weakly np-complete. We demonstrate how these findings contradict the generally accepted assumption of a single analytic functional. Third, we analyze and quantify the relations between the number of subdomains and the spectrum of a generic interaction.