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Linked cluster expansions via hypergraph decompositions.

Matthias Mühlhauser1, Kai Phillip Schmidt1

  • 1Department of Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstrasse 7, D-91058 Erlangen, Germany.

Physical Review. E
|July 20, 2022
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Summary
This summary is machine-generated.

We developed a hypergraph expansion for quantum spin models with many-site interactions. This method efficiently calculates ground-state energy and excitation gaps, simplifying complex quantum system analysis.

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Area of Science:

  • Quantum physics
  • Condensed matter theory
  • Computational physics

Background:

  • Quantum spin models with many-site interactions present significant computational challenges.
  • Perturbative linked cluster expansions are a common tool but can be complex to apply to intricate models.

Purpose of the Study:

  • To introduce a novel hypergraph expansion method for directly treating quantum spin models with many-site interactions.
  • To simplify the application of perturbative linked cluster expansions to complex quantum systems.

Main Methods:

  • A hypergraph expansion is proposed, generating and sorting subclusters into equivalence classes based on hypergraph isomorphism.
  • A reduced König representation is employed to facilitate graph isomorphism checks for equivalence relations.
  • Embedding factors for each equivalence class are determined for the final resummation.

Main Results:

  • The method successfully calculates the ground-state energy of the plaquette Ising model in a transverse field on a 3D cubic lattice.
  • A specific excitation gap for the same model system was also accurately determined.

Conclusions:

  • The proposed hypergraph expansion offers an efficient and direct approach to studying quantum spin models with complex interactions.
  • This technique provides a powerful tool for analyzing the properties of various quantum many-body systems.