Berlin 2024 – wissenschaftliches Programm

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TT: Fachverband Tiefe Temperaturen

TT 80: Correlated Electrons: Poster

TT 80.46: Poster

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

Hypergraph Decompositions — •Matthias Mühlhauser and Kai Phillip Schmidt — Friedrich-Alexander-Universität Erlangen-Nürnberg

A crucial element of graph-based linked-cluster expansions is to identify structurally equivalent clusters. To this end the clusters are typically represented by graphs, where the vertices represent the sites and the edges represent the couplings between the sites. The structural equivalence of clusters corresponds to isomorphism of the respective graphs.

However, if (possibly oriented) many-site couplings exist such a graph representation is typically not obvious, whereas hypergraphs naturally capture this structure. Interestingly, it is known that hypergraphs can be unambigously represented by bipartite graphs. We exploit this representation to distinguish equivalence classes of clusters and set up linked-cluster expansions via full hypergraph decompositions [1].

[1] Phys. Rev. E 105, 064110

Keywords: Linked Cluster; Perturbation Theory; Graph; Hypergraph