Multipartite information of free fermions on Hamming graphs

We investigate multipartite information and entanglement measures in the ground state of a free-fermion model defined on a Hamming graph. Using the known diagonalization of the adjacency matrix, we solve the model and construct the ground-state correlation matrix. Moreover, we find all the eigenvalu...

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Bibliographic Details
Published in:Nuclear physics. B 2023-05, Vol.990, p.116157, Article 116157
Main Authors: Parez, Gilles, Bernard, Pierre-Antoine, Crampé, Nicolas, Vinet, Luc
Format: Article
Language:English
Subjects:
Condensed Matter
Mathematical Physics
Physics
Quantum Physics
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Summary:We investigate multipartite information and entanglement measures in the ground state of a free-fermion model defined on a Hamming graph. Using the known diagonalization of the adjacency matrix, we solve the model and construct the ground-state correlation matrix. Moreover, we find all the eigenvalues of the chopped correlation matrix when the subsystem consists of n disjoint Hamming subgraphs embedded in a larger one. These results allow us to find an exact formula for the entanglement entropy of disjoint graphs, as well as for the mutual and tripartite information. We use the exact formulas for these measures to extract their asymptotic behavior in two distinct thermodynamic limits, and find excellent match with the numerical calculations. In particular, we find that the entanglement entropy admits a logarithmic violation of the area law which decreases the amount of entanglement compared to the area law scaling.
ISSN:0550-3213
1873-1562
DOI:10.1016/j.nuclphysb.2023.116157