Multipartite information of free fermions on Hamming graphs

TL;DR

This paper derives exact formulas for multipartite entanglement measures in a free-fermion model on Hamming graphs, revealing a logarithmic violation of the area law and providing insights into entanglement scaling in complex quantum systems.

Contribution

It provides the first exact formulas for entanglement entropy and information measures in free fermions on Hamming graphs, including asymptotic analysis and numerical validation.

Findings

Exact formulas for entanglement entropy, mutual, and tripartite information.

Logarithmic violation of the area law in entanglement entropy.

Strong agreement between analytical results and numerical calculations.

Abstract

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.