Entanglement of free fermions on Hamming graphs

Free fermions on Hamming graphs H(d, q) are considered and the entanglement entropy for two types of subsystems is computed. For subsets of vertices that form Hamming subgraphs, an analytical expres-sion is obtained. For subsets corresponding to a neighborhood, i.e. to a set of sites at a fixed distance from a reference vertex, a decomposition in irreducible submodules of the Terwilliger algebra of H(d, q) also yields a closed formula for the entanglement entropy. Finally, for subsystems made out of multiple neigh-borhoods, it is shown how to construct a block-tridiagonal operator which commutes with the entanglement Hamiltonian. It is identified as a BC-Gaudin magnet Hamiltonian in a magnetic field and is diagonalized by the modified algebraic Bethe ansatz.(c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3.

Automated summary

This article focuses on free fermions on Hamming graphs H(d, q) and computes the entanglement entropy for two types of subsystems. An analytical expression is obtained for subsets of vertices that form Hamming subgraphs. For subsets corresponding to a neighborhood, a decomposition in irreducible submodules of the Terwilliger algebra of H(d, q) also yields a closed formula for the entanglement entropy. The article also shows how to construct a block-tridiagonal operator for subsystems made out of multiple neighborhoods, which commutes with the entanglement Hamiltonian and is identified as a BC-Gaudin magnet Hamiltonian in a magnetic field and is diagonalized by the modified algebraic Bethe ansatz.