Linked cluster expansions via hypergraph decompositions

Mühlhauser M, Schmidt KP (2022)

Publication Type: Journal article

Publication year: 2022


Book Volume: 105

Journal Issue: 6

DOI: 10.1103/PhysRevE.105.064110


We propose a hypergraph expansion which facilitates the direct treatment of quantum spin models with many-site interactions via perturbative linked cluster expansions. The main idea is to generate all relevant subclusters and sort them into equivalence classes essentially governed by hypergraph isomorphism. Concretely, a reduced K??nig representation of the hypergraphs is used to make the equivalence relation accessible by graph isomorphism. During this procedure we determine the embedding factor for each equivalence class, which is used in the final resummation in order to obtain the final result. As an instructive example we calculate the ground-state energy and a particular excitation gap of the plaquette Ising model in a transverse field on the three-dimensional cubic lattice.

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How to cite


Mühlhauser, M., & Schmidt, K.P. (2022). Linked cluster expansions via hypergraph decompositions. Physical Review E, 105(6).


Mühlhauser, Matthias, and Kai Phillip Schmidt. "Linked cluster expansions via hypergraph decompositions." Physical Review E 105.6 (2022).

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